Preprints and Publications 2

Surveys and Book Chapters

• J. A. Carrillo, D. Matthes, M.-T. Wolfram, Lagrangian schemes for Wasserstein gradient flows, Chapter 4, Handbook of Numerical Analysis 22, 271-311, Elsevier, 2021.
• J. A. Carrillo, K. Craig, Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, in N. Bellomo, P. Degond, and E. Tadmor (Eds.), Active Particles Vol. II: Advances in Theory, Models, and Applications, Series: Modelling and Simulation in Science and Technology, Birkhäuser Basel, 65-108, 2019.
• R. Bailo, J. A. Carrillo, P. Degond, Pedestrian Models based on Rational Behaviour, in: Gibelli L., Bellomo N. (eds) Crowd Dynamics, Volume 1. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham, 259-292, 2018. Supplementary Material: Movies and Simulations.
• V. Calvez, J. A. Carrillo, F. Hoffmann, The geometry of diffusing and self-attracting particles in a one-dimensional fair-competition regime, Lecture Notes in Mathematics 2186, CIME Foundation Subseries, Springer, 2018.
• J. A. Carrillo, Y.-P. Choi, S. Pérez, A review on attractive-repulsive hydrodynamics for consensus in collective behavior, in N. Bellomo, P. Degond, and E. Tadmor (Eds.), Active Particles Vol. I: Advances in Theory, Models, and Applications, Series: Modelling and Simulation in Science and Technology, Birkhäuser Basel, 259-298, 2017.
• J. A. Carrillo, Y.-P. Choi, M. Hauray, The derivation of Swarming models: Mean-Field Limit and Wasserstein distances, Collective Dynamics from Bacteria to Crowds: An Excursion Through Modeling, Analysis and Simulation Series, CISM International Centre for Mechanical Sciences, Vol. 553, 1-46, 2014.
• J. A. Carrillo, M. Fornasier, G. Toscani, F. Vecil, Particle, Kinetic, and Hydrodynamic Models of Swarming, in Naldi, G., Pareschi, L., Toscani, G. (eds.) Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, Series: Modelling and Simulation in Science and Technology, Birkhauser, (2010), 297-336.
• J. A. Carrillo, G. Toscani, Contractive Probability Metrics and Asymptotic Behavior of Dissipative Kinetic Equations, Notes of the 2006 Porto Ercole Summer School, Rivista Matemàtica di Parma 6, 75-198, 2007.

Aggregation-Diffusion Equations and Keller-Segel models:  Analysis

• J. A. Carrillo, A. Fernández-Jiménez, D. Gómez-Castro, Partial mass concentration for fast-diffusions with non-local aggregation terms, Preprint.
• J. A. Carrillo, Y. Peng, Z. Xiang, Global existence and decay rates to self-consistent chemotaxis-fluid system, Preprint.
• J. A. Carrillo, D. Gómez-Castro, Y. Yao, C. Zeng, Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel, to appear in Arch. Rat. Mech. Anal.
• J. A. Carrillo,  D. Gómez-Castro, J. L. Vázquez, Infinite-time concentration in Aggregation–Diffusion equations with a given potential, J. Math. Pures et Appl. 157, 346-398, 2022.
• J. A. Carrillo, M. G. Delgadino, R. L. Frank, M. Lewin, Fast Diffusion leads to partial mass concentration in Keller-Segel type stationary solutions, Math. Models Methods Appl. Sci. 32, 831–850, 2022.
• J. A. Carrillo, D. Gómez-Castro, J. L. Vázquez, Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility, Adv. Nonlinear Anal. 11, 937–967, 2022. Supplementary Material: Movies and Simulations.
• J. A. Carrillo, R. S. Gvalani, J. Wu, An invariance principle for gradient flows in the space of probability measures, J. Diff. Eqns. 345, 233-284, 2023.
• M. Bruna, M. Burger, J. A. Carrillo, Coarse graining of a Fokker-Planck equation with excluded volume effects preserving the gradient-flow structure, European J. Appl. Math. 32, 711-745, 2021.
• J. A. Carrillo, B. Düring, L. M, Kreusser, C.-B. Schönlieb, Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics, DCDS-A 41, 3985-4012, 2021.
• J. A. Carrillo, R. S. Gvalani, Phase transitions for nonlinear nonlocal aggregation-diffusion equations, Comm. Math. Phys. 382, 485-545, 2021.
• J. A. Carrillo, D. Gómez-Castro, J. L. Vázquez, A fast regularisation of a Newtonian vortex equation, Ann. Inst. H. Poincaré C Anal. Non Linéaire 39, 705–747, 2022.
• V. Calvez, J. A. Carrillo, F. Hoffmann, Uniqueness of stationary states for singular Keller-Segel type models, Nonlinear Analysis TMA 205, 112222, 2021.
• J. A. Carrillo, E. A. Pimentel, V. K. Voskanyan, On a Mean Field Optimal Control Problem, Nonlinear Analysis: TMA 199, 112039, 2020.
• J. A Carrillo, J. Li, Z. Wang, Boundary spike-layer solutions of the singular Keller-Segel system: existence and stability, Proceedings of the LMS 122, 42-68, 2021.
• J. A. Carrillo, M. G. Delgadino, G. A. Pavliotis, A  λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles, J. Functional Analysis 279, 108734, 2020.
• J. A. Carrillo, X. Chen, Q. Wang, Z. Wang, L. Zhang, Phase transitions and bump solutions of the Keller-Segel model with volume exclusion, SIAM J. Applied Mathematics 80, 232-261, 2020.
• J. A. Carrillo, K. Hopf, J. L. Rodrigo, On the singularity formation and relaxation to equilibrium in 1D Fokker-Planck model with superlinear drift, Adv. Math. 360, 106883, 2020.
• J. A. Carrillo, R. S. Gvalani, G. A. Pavliotis, A. Schlichting, Long-time behaviour and phase transitions for the McKean–Vlasov equation on the torus, Arch. Rat. Mech. Anal. 235, 635-690, 2020.
• J. A. Carrillo, K. Craig, Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, in N. Bellomo, P. Degond, and E. Tadmor (Eds.), Active Particles Vol. II: Advances in Theory, Models, and Applications, Series: Modelling and Simulation in Science and Technology, Birkhäuser Basel, 65-108, 2019.
• J. A. Carrillo, S. Hittmeir, B. Volzone, Y. Yao, NonlinearAggregation-Diffusion Equations: Radial Symmetry and Long Time Asymptotics, Inventiones Mathematicae 218, 889-977, 2019.
• L. Alasio, M. Bruna, J. A. Carrillo, The role of a strong confining potential in a nonlinear Fokker-Planck equation, Nonlinear Analysis TMA 193, 111480, 2020.
• J. A. Carrillo, M. G. Delgadino, J. Dolbeault, R. L. Frank, F. Hoffmann, Reverse Hardy-Littlewood-Sobolev inequalities, J. Math. Pure Appl. 132, 133–165, 2019.
• J. A. Carrillo, B. Düring, L. M, Kreusser, C.-B. Schönlieb, Stability analysis of line patterns of an anisotropic interaction model, SIAM J. Dyn. Sys. 18, 1798-1845, 2019.
• J. A. Carrillo, M. Delgadino, F. S. Patacchini, Existence of ground states for aggregation-diffusion equations, Analysis and Applications 17, 393-423, 2019.
• J. A. Carrillo, J. Wang, Uniform in time Linfty-estimates for nonlinear aggregation-diffusion equations, Acta Appl. Math. 164, 1–19, 2019.
• V. Calvez, J. A. Carrillo, F. Hoffmann, The geometry of diffusing and self-attracting particles in a one-dimensional fair-competition regime, Lecture Notes in Mathematics 2186, CIME Foundation Subseries, Springer, 2018.
• J. A. Carrillo, F. Santambrogio, L^∞ estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems, Quarterly of Applied Mathematics 3, 515-530, 2018.
• J. A. Carrillo, F. Hoffmann, E. Mainini, B. Volzone, Ground States in the Diffusion-Dominated Regime, Calc. Var. Partial Differential Equations 57, 57-127, 2018.
• J. A. Carrillo, Y. Sugiyama, Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime, Indiana Univ. Math. J. 67, 2279-2312, 2018.
• V. Calvez, J. A. Carrillo, F. Hoffmann, Equilibria of homogeneous functionals in the fair-competition regime, Nonlinear Analysis TMA 159, 85-128, 2017.
• J. A. Carrillo, J. L. Vázquez, Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation, Phil. Trans. R. Soc. A 373, 20140275, 2015.
• A. Blanchet, J. A. Carrillo, D. Kinderlehrer, M. Kowalczyk, P. Laurençot, S. Lisini, A hybrid variational principle for the Keller-Segel system in R2, M2AN 49, 1553-1576, 2015.
• J. A. Carrillo, D. Castorina, B. Volzone, Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction, SIAM J. Math. Anal. 47, 1-25, 2015.
• J. A. Carrillo, S. Lisini, E. Mainini, Uniqueness for Keller-Segel-type chemotaxis models, Discrete and Continuous Dynamical Systems-A 34, 1319-1338, 2014.
• J. A. Carrillo, S. Hittmeir, A. Jüngel, Cross diffusion and nonlinear diffusion preventing blow up in the Keller-Segel model, Math. Mod. Meth. Appl Sci. 22, 1250041, 2012.
• J. A. Carrillo, L. Chen, J.-G. Liu, and J. Wang, A note on the subcritical two dimensional Keller-Segel System, Acta Applicandae Mathematicae 119, 43-55, 2012.
• A. Blanchet, E. A. Carlen, J. A. Carrillo, Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model, J. Func. Anal. 262, 2142-2230, 2012.
• V. Calvez, J. A. Carrillo, Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities, Proc. AMS. 140, 3515-3530, 2012.
• E. A. Carlen, J. A. Carrillo, M. Loss, Hardy-Littlewood-Sobolev inequalities via fast diffusion flows, Proc. Nat. Acad. USA 107 (46), 19696-19701, 2010.
• A. Blanchet, J. A. Carrillo, P. Laurençot, Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions, Calculus of Variations and PDEs 35, 133-168, 2009.
• A. Blanchet, V. Calvez, J. A. Carrillo, Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model, SIAM J. Numer. Anal. 46, 691–721, 2008.
• A. Blanchet, J. A. Carrillo, N. Masmoudi, Infinite Time Aggregation for the Critical PKS model in R2, Comm. Pure and Applied Mathematics 61, 1449-1481, 2008.
• V. Calvez, J.A. Carrillo, Volume effects in the Keller-Segel model: energy estimates preventing blow-up, Journal Mathématiques Pures et Appliquées 86, 155-175, 2006.

Aggregation Equations and Interaction Energies:  Analysis

• J. A. Carrillo, A. Esposito, J. S.-H. Wu, Nonlocal approximation of nonlinear diffusion equations, Preprint.
• J. A. Carrillo, R. Shu, Minimizers of 3D anisotropic interaction energies, Preprint.
• J. A. Carrillo, R. Shu, Global Minimizers of a Large Class of Anisotropic Attractive-Repulsive Interaction Energies in 2D, to appear in Comm. Pure App. Math.
• J. A. Carrillo, R. Shu, From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials, Calc. Var. Partial Differential Equations 62, 28, 2023.
• J. A. Carrillo, J. Mateu, M.G. Mora, L. Rondi, L. Scardia, J. Verdera, The equilibrium measure for an anisotropic nonlocal energy, Cal. Var. PDE 60, 109, 2021.
• J. A. Carrillo, J. Mateu, M.G. Mora, L. Rondi, L. Scardia, J. Verdera, The ellipse law: Kirchhoff meets dislocations, Comm. Math. Phys. 373, 507-524, 2020.
• J. A. Carrillo, A. Figalli, F. S. Patacchini, Geometry of minimizers for the interaction energy with mildly repulsive potentials, Ann. IHP 34, 1299-1308, 2017.
• J. A. Carrillo, Y. Huang, Explicit Equilibrium Solutions For the Aggregation Equation with Power-Law Potentials, Kinetic Rel. Mod. 10, 171-192, 2017.   
• J. A. Carrillo, F. James, F. Lagoutière, N. Vauchelet, The Filippov characteristic flow for the aggregation equation with mildly singular potentials, J. Differential Equations 260, 304-338, 2016.
• J. A. Carrillo, M. G. Delgadino, A. Mellet, Regularity of local minimizers of the interaction energy via obstacle problems, Comm. Math. Phys. 343, 747-781, 2016.
• J. A. Carrillo, D. Slepčev, L. Wu, Nonlocal-interaction equations on uniformly prox-regular sets, Discrete and Continuous Dynamical Systems-A 36, 1209-1247, 2016.
• J. A. Carrillo, M. DiFrancesco, G. Toscani, Condensation phenomena in nonlinear drift equations, Annali della Scuola Normale Superiore di Pisa XV, 145-171, 2016.
• J. A. Cañizo, J. A. Carrillo, F. S. Patacchini, Existence of Compactly Supported Global Minimisers for the Interaction Energy, Arch. Rat. Mech. Anal. 217, 1197-1217, 2015.
• G. A. Bonaschi, J. A. Carrillo, M. DiFrancesco, M. A. Peletier, Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D, ESAIM: Control, Optimization and Calculus of Variations 21, 414–441, 2015.
• J. A. Carrillo, M. Chipot, Y. Huang, On global minimizers of repulsive-attractive power-law interaction energies, Philosophical Transactions of the Royal Society A 372, 20130399, 2014.
• D. Balagué, J. A. Carrillo, T. Laurent, G. Raoul, Dimensionality of Local Minimizers of the Interaction Energy, Archive for Rational Mechanics and Analysis 209, 1055–1088, 2013.
• D. Balagué, J. A. Carrillo, Y. Yao, Confinement for Repulsive-Attractive Kernels, Discrete and Continuous Dynamical Systems-B 19, 1227–1248, 2014.
• J. A. Carrillo, S. Lisini, E. Mainini, Gradient flows for non-smooth interaction potentials, Nonlinear Analysis TMA 100, 122–147, 2014.
• J. A. Carrillo, L. C. F. Ferreira, J. C. Precioso, A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity, Advances in Mathematics 231, 306-327, 2012.
• D. Balagué, J. A. Carrillo, T. Laurent, G. Raoul, Nonlocal interactions by repulsive-attractive potentials: radial ins/stability, Physica D 260, 5-25, 2013.
• J. A. Carrillo, M. DiFrancesco, A. Figalli, T. Laurent, D. Slepcev, Confinement in nonlocal interaction equations, Nonlinear Analysis TMA 75, 550-558, 2012.
• D. Balagué, J. A. Carrillo, Aggregation equation with growing at infinity attractive-repulsive potential, Proceedings of the 13th International Conference on Hyperbolic Problems, Series in Contemporary Applied Mathematics CAM 17, Higher Education Press, Volume 1, 136-147, 2012.
• J. A. Carrillo, M. DiFrancesco, A. Figalli, T. Laurent, D. Slepcev, Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations, Duke Math. J. 156, 229-271, 2011.
• J. A. Carrillo, J. Rosado, Uniqueness of Bounded Solutions to Aggregation Equations by Optimal Transport Methods, Proceedings of the 5th European Congress of Mathematicians, 3–16, Eur. Math. Soc., Zurich, 2010.
• A. L. Bertozzi, J. A. Carrillo, T. Laurent, Blowup in multidimensional aggregation equations with mildly singular interaction kernels, Nonlinearity 22, 683-710, 2009.

Aggregation-Diffusion Equations:  Numerical Analysis and Scientific Computing

• T. S. Gutleb, J. A. Carrillo, A static memory sparse spectral method for time-fractional PDEs in arbitrary dimensions, Preprint.
• J. A. Carrillo, L. Wang, C. Wei, Structure preserving primal dual methods for gradient flows with nonlinear mobility transport distances, Preprint.
• R. Bailo, J. A. Carrillo, J. Hu, Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation, to appear in SIAM J. Appl. Math.
• T. S. Gutleb, J. A. Carrillo, S. Olver, Computation of Power Law Equilibrium Measures on Balls of Arbitrary Dimension, to appear in Cons. Approx.
• T. S. Gutleb, J. A. Carrillo, S. Olver, Computing Equilibrium Measures with Power Law Kernels, to appear in Mathematics of Computation.
• J. A. Carrillo, L. Chen, Q. Wang, An Optimal Mass Transport Method for Random Genetic Drift, SIAM J. Numer. Anal. 60, 940–969, 2022.
• J. A. Carrillo, D. Matthes, M.-T. Wolfram, Lagrangian schemes for Wasserstein gradient flows, Chapter 4, Handbook of Numerical Analysis 22, 271-311, Elsevier, 2021.
• R. Bailo, J. A. Carrillo, H. Murakawa, M. Schmidtchen, Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations, Math. Mod. Meth. Appl. Sci. 30, 2487-2522, 2020.
• J. A. Carrillo, K. Craig, L. Wang, C. Wei, Primal dual methods for Wasserstein gradient flows, Found. Comput. Math. 22, 389–443, 2022. Supplementary Material: Movies and Simulations.
• J.A. Carrillo, K. Hopf, M.-T. Wolfram, Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosons, Kinetic and Related Models 13, 507-529, 2020.
• R. Bailo, J. A. Carrillo, J. Hu, Fully Discrete Positivity-Preserving and Energy-Decaying Schemes for Aggregation-Diffusion Equations with a Gradient Flow Structure, Comm. Math. Sci. 18, 1259–1303, 2020. 
• J. A. Carrillo, Y.-P. Choi, L. Pareschi, Structure preserving schemes for the continuum Kuramoto model: phase transitions, J. Comp. Phys. 376, 365-389, 2019.
• J. A. Carrillo, K. Craig, F. S. Patacchini, A Blob Method For Diffusion, Calc. Var. Partial Differential Equations 58, Art. 53, 2019.
• Z. Sun, J. A. Carrillo, C.-W. Shu, An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems, Kinetic Rel. Mod. 12, 885-908, 2019.
• J. A. Carrillo, U. S. Fjordholm, S. Solem, A second-order numerical method for the aggregation equations, Math. Comp. 90, 103–139, 2021.
• J. A. Carrillo, N. Kolbe, M. Lukácová-Medvidová, A hybrid mass transport finite element method for Keller–Segel type systems, J. Sci. Comp. 80, 1777-1804, 2019.
• Z. Sun, J. A. Carrillo, C.-W. Shu, A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials, J. Comp. Phys. 352, 76-104, 2018.
• J. A. Carrillo, A. Jüngel, M. C. Santos, Displacement convexity for the entropy in semidiscrete nonlinear Fokker-Planck equations, European J. Appl. Math. 1103-1122, 2019.
• J. A. Carrillo, B. Düring, D. Matthes, D. S. McCormick, A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes, J. Sci. Computing 75, 1463-1499, 2018.
• M. Campos-Pinto, J. A. Carrillo, F. Charles, Y.-P. Choi, Convergence of a Linearly Transformed Particle Method for Aggregation Equations, Numerische Mathematik 139, 743-793, 2018.
• J. Barré, J. A. Carrillo, P. Degond, D. Peurichard, E. Zatorska, Particle interactions mediated by dynamical networks: assessment of macroscopic descriptions, J. Nonlinear Sci. 28, 235–268, 2018.
• J. A. Carrillo, F. S. Patacchini, P. Sternberg, G. Wolansky, Convergence of a particle method for diffusive gradient flows in one dimension, SIAM J. Math. Analysis 48, 3708-3741, 2016.
• J. A. Carrillo, H. Ranetbauer, M.-T. Wolfram, Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms, J. Comp. Phys. 327, 186-202, 2016.
• J. A. Carrillo, Y. Huang, F. S. Patacchini, G. Wolansky, Numerical Study of a Particle Method for Gradient Flows, Kinetic Rel. Mod. 10, 613-641, 2017.
• J. A. Carrillo, A. Chertock, Y. Huang, A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure, Comm. in Comp. Phys. 17, 233-258, 2015.
• M. Burger, J. A. Carrillo, M.-T. Wolfram, A Mixed Finite Element Method for Nonlinear Diffusion Equations, Kinetic and Related Models 3, 59-83, 2010.
• J. A. Carrillo, J. S. Moll, Numerical simulation of diffusive and aggregation phenomena in nonlinear continuity equations by evolving diffeomorphisms, SIAM J. Sci. Comput. 31, 4305-4329, 2009.
• J.A. Carrillo, A. Jungel, S. Tang, Positive Entropic Schemes for a Nonlinear Fourth-order Parabolic Equation, Discrete and Continuous Dynamical Systems B 3, 1-20, 2003.

Aggregation-Diffusion Systems: Analysis

Aggregation-Diffusion Systems: Applications in Cell Sorting and Adhesion

• C. Falcó, D. J. Cohen, J. A. Carrillo, R. E. Baker, Quantifying tissue growth, shape and collision via continuum models and Bayesian inference, Preprint.
• C. Falcó, R. E. Baker, J. A. Carrillo, A local continuum model of cell-cell adhesion, to appear in SIAM J. Appl. Math.
• O. Trush, C. Liu, X. Han, Y. Nakai, R. Takayama, H. Murakawa, J. A. Carrillo, H. Takechi, S. Hakeda-Suzuki, T. Suzuki, M. Sato, N-cadherin orchestrates self-organization of neurons within a columnar unit in the Drosophila medulla, J. Neuroscience 39, 5861-5880, 2019.
• J. A. Carrillo, H. Murakawa, M. Sato, H. Togashi, O. Trush, A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation, J. Theor. Biology 474, 14-24, 2019. Supplementary Material: Movies and Simulations.
• A. Gosztolai, J. A. Carrillo, M. Barahona, Collective search with finite perception: transient dynamics and search efficiency, Frontiers in Physics 6, 153-163, 2019.
• J. A. Carrillo, A. Colombi, M. Scianna, Adhesion and volume constraints via nonlocal interactions lead to cell sorting, J. Theo. Biology 445, 75-91, 2018.

Kinetic Equations in Plasmas

• J. A. Carrillo, M. G. Delgadino, J. S. H. Wu, Convergence of a particle method for a regularized spatially homogeneous Landau equation, Math. Mod. Meth. Appl. Sci. 33, 971-1008, 2023.
• J. A. Carrillo, S. Jin, Y. Tang, Random batch particle methods for the homogeneous Landau equation, Commun. Comput. Phys. 31, 997-1019, 2022.
• J. A. Carrillo, M. Delgadino, J. Wu, Boltzmann to Landau from the Gradient Flow Perspective, Nonlinear Anal. 219, Paper No. 112824, 2022.
• J. A. Carrillo, M. G. Delgadino, L. Desvillettes, J. Wu, The Landau equation as a Gradient Flow, to appear in Analysis & PDE.
• J. A. Carrillo, J. Hu, L. Wang, J. Wu, A particle method for the homogeneous Landau equation, J. Comp. Phys. X 7, 100066, 2020.
• J.A. Carrillo, F. Vecil, Non oscillatory interpolation methods applied to Vlasov-based models, SIAM Journal of Scientific Computing 29, 1179-1206, 2007.
• S. Labrunie, J.A. Carrillo, P. Bertrand, Numerical study on hydrodynamic and quasi-neutral approximations for collisionless two-species plasmas, Journal of Computational Physics 200, 267-298, 2004.

PDE Models in Large Data Optimisation and Sampling

• J. A. Carrillo, N. Garcia-Trillos, S. Li, Y. Zhu, FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization, Preprint.
• J. A. Carrillo, F. Hoffmann, A. M. Stuart, U. Vaes, The Ensemble Kalman Filter in the Near-Gaussian Setting, Preprint.
• J. A. Carrillo, C. Totzeck, U. Vaes, Consensus-based Optimization and Ensemble Kalman Inversion for Global Optimization Problems with Constraints, in: Modeling and Simulation for Collective Dynamics, Lecture Notes Series, Institute for Mathematical Sciences, NUS: Volume 40, 2023.
• J. A. Carrillo, F. Hoffmann, A. M. Stuart, U. Vaes, Consensus Based Sampling, Stud. Appl. Math. 148, 1069–1140, 2022. Supplementary Material: Movies and Simulations.
• J.A. Carrillo, U. Vaes, Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations, Nonlinearity 34, 2275-2295, 2021.
• J. A. Carrillo, S. Jin, L. Li, Y. Zhu, A consensus-based global optimization method for high dimensional machine learning problems, ESAIM Control Optim. Calc. Var. 27, Paper No. S5, 2021.
• J. A. Carrillo, Y.-P. Choi, C. Totzeck, O. Tse, An analytical framework for a consensus-based global optimization method, Mathematical Models and Methods in the Applied Sciences 28, 1037-1066, 2018.

Particle and PDE Models in Collective Behavior

• A. J. King, S. J. Portugal, D. Strömbom, R. P. Mann, J. A. Carrillo, D. Kalise, G. de Croon, H. Barnett, P. Scerri, R. Gross, D. Chadwick, M. Papadopolou, Biologically inspired herding of animal groups by robots, to appear in Methods in Ecology and Evolution.
• J. A. Carrillo, D. Kalise, F. Rossi, E. Trélat, Controlling swarms towards flocks and mills, SIAM J. Control and Optimization 60, 1863-1891, 2022.
• J. A. Carrillo, Y.-P. Choi, Mean-field limits: from particle descriptions to macroscopic equations, Arch. Rat. Mech. Anal. 241, 1529-1573, 2021.
• A. Barbaro, D. Balagué, J. A. Carrillo, R. Volkin, Analysis of spherical shell solutions for the radially symmetric Aggregation Equation, SIAM J. Appl. Dyn. Sys. 9, 2628-2657, 2020.
• J. A. Carrillo, M. Zanella, Monte Carlo gPC methods for diffusive kinetic flocking models with uncertainties, Vietnam Journal of Mathematics 47, 931-954, 2019.
• J. A. Carrillo, L. Pareschi, M. Zanella, Particle based gPC methods for mean-field models of swarming with uncertainty, Comm. in Comp. Phys. 25, 508-531, 2019.
• J. A. Carrillo, Y.-P. Choi, M. Hauray, S. Salem, Mean-field limit for collective behavior models with sharp sensitivity regions, J. European Math. Soc. 21, 121-161, 2019.
• R. Bailo, J. A. Carrillo, P. Degond, Pedestrian Models based on Rational Behaviour, in: Gibelli L., Bellomo N. (eds) Crowd Dynamics, Volume 1. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham, 259-292, 2018. Supplementary Material: Movies and Simulations.
• R. Bailo, M. Bongini, J. A. Carrillo, D. Kalise, Optimal consensus control of the Cucker-Smale model, IFAC-PapersOnLine 51, 1-6, 2018.
• J. A. Carrillo, Y.-P. Choi, P. B. Mucha, J. Peszek, Sharp conditions to avoid collisions in singular Cucker-Smale interactions, Nonlinear Analysis Series B: Real World Applications 37, 317-328, 2017.
• A. B. T. Barbaro, J. A. Cañizo, J. A. Carrillo, P. Degond, Phase Transitions in a kinetic flocking model of Cucker-Smale type, Multiscale Model. Simul. 14, 1063-1088, 2016.
• J. A. Carrillo, A. Klar, A. Roth, Single to Double Mill Small Noise Transition via Semi-Lagrangian Finite Volume Methods, Comm. Math. Sci. 14, 1111-1136, 2016.
• J. A. Carrillo, R. Eftimie, F. K. O. Hoffmann, Non-local kinetic and macroscopic models for self-organised animal aggregations, Kinetic and Related Models 8, 413-441, 2015.
• J. A. Carrillo, Y.-P. Choi, M. Hauray, Local well-posedness of the generalized Cucker-Smale model with singular kernels, ESAIM: Proceedings and Surveys 47, 17-35, 2014.
• J. A. Carrillo, Y.-P. Choi, M. Hauray, The derivation of Swarming models: Mean-Field Limit and Wasserstein distances, Collective Dynamics from Bacteria to Crowds: An Excursion Through Modeling, Analysis and Simulation Series, CISM International Centre for Mechanical Sciences, Vol. 553, 1-46, 2014.
• J. A. Carrillo, Y. Huang, S. Martin, Nonlinear stability of flock solutions in second-order swarming models, Nonlinear Analysis: Real World Applications 17, 332–343, 2014.
• J. A. Carrillo, Y. Huang, S. Martin, Explicit Flock Solutions for Quasi-Morse potentials, European Journal of Applied Mathematics 25, 553–578, 2014.
• G. Albi, D. Balagué, J. A. Carrillo, J. von Brecht, Stability Analysis of Flock and Mill rings for 2nd Order Models in Swarming, SIAM J. Appl. Math. 74, 794–818, 2014.
• T. Kolokolnikov, J. A. Carrillo, A. Bertozzi, R. Fetecau, M. Lewis, Emergent behaviour in multi-particle systems with non-local interactions, Phys. D 260, 1-4, 2013.
• J. A. Carrillo, S. Martin, V. Panferov, A new interaction potential for swarming models, Physica D 260, 112-126, 2013.
• M. Bostan, J. A. Carrillo, Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming, Math. Mod. Meth. in the Appl. Sci. 23, 2353, 2013.
• F. Bolley, J. A. Cañizo, J. A. Carrillo, Mean-field limit for the stochastic Vicsek model, Appl. Math. Letters 25, 339-343, 2012.
• F. Bolley, J. A. Cañizo, J. A. Carrillo, Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming, Math. Mod. Meth. Appl. Sci. 21, 2179-2210, 2011.
• J. A. Carrillo, A. Klar, S. Martin, S. Tiwari, Self-propelled interacting particle systems with roosting force, Math. Mod. Meth. Appl. Sci. 20, 1533-1552, 2010.
• J. A. Cañizo, J. A. Carrillo, J. Rosado, A well-posedness theory in measures for some kinetic models of collective motion, Math. Mod. Meth. Appl. Sci. 21, 515-539, 2011.
• J. A. Carrillo, M. Fornasier, J. Rosado, G. Toscani, Asymptotic Flocking Dynamics for the kinetic Cucker-Smale model, SIAM J. Math. Anal. 42, 218-236, 2010.
• J. A. Cañizo, J. A. Carrillo, J. Rosado, Collective Behavior of Animals: Swarming and Complex Patterns, Arbor 186, 1035-1049, 2010.
• J. A. Carrillo, M. Fornasier, G. Toscani, F. Vecil, Particle, Kinetic, and Hydrodynamic Models of Swarming, in Naldi, G., Pareschi, L., Toscani, G. (eds.) Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, Series: Modelling and Simulation in Science and Technology, Birkhauser, (2010), 297-336.
• J. A. Carrillo, M. R. D’Orsogna, V. Panferov, Double milling in self-propelled swarms from kinetic theory, Kinetic and Related Models 2, 363-378, 2009.

Fluid Models in Collective Behavior: Analysis, Numerics and modelling

• J. A. Carrillo, R. Shu, Existence of radial global smooth solutions to the pressureless Euler-Poisson equations with quadratic confinement, Preprint.
• J. A. Carrillo, Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Dissipative measure-valued solutions to the Euler-Poisson equation, Preprint.
• F. Magaletti, M. Gallo, S. P. Perez, J. A. Carrillo, S. Kalliadasis, A positivity-preserving scheme for fluctuating hydrodynamics, Journal of Computational Physics 463, 111248, 2022.
• J. A. Carrillo, Y.-P. Choi, J. Jung, Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces,  Math. Mod. Meth. Appl. Sci. 31, 327-408, 2021.
• J. A. Carrillo, M. J. Castro, S. Kalliadasis, S. P. Perez, High-order well-balanced finite volume schemes for hydrodynamic equations with nonlocal free energy, SIAM J. Sci. Computing 43, A828–A858, 2021.
• M. Bostan, J. A. Carrillo, Fluid models with phase transition for kinetic equations in swarming, Math. Models and Meth. in the Appl. Sci. 30, 2023–2065, 2020.
• J. A. Carrillo, Y. Peng, A. Wróblewska-Kaminska, Relative Entropy Method for the relaxation limit of Hydrodynamic models, Networks and Heterogeneous Media 15, 369-387, 2020.
• A. Russo, S. P. Perez, M. A. Duran-Olivencia, P. Yatsyshin, J. A. Carrillo, S. Kalliadasis, A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory, J. Comp. Phys. 428, 109796, 2021.
• J. A. Carrillo, A. Wróblewska-Kaminska, E. Zatorska, Pressureless Euler with nonlocal interactions as a singular limit of degenerate Navier-Stokes system, J. Math. Anal. Appl. 492, 124400, 2020.
• J. A. Carrillo, S. Kalliadasis, S. P. Perez, C.-W. Shu, Well-balanced finite volume schemes for hydrodynamic equations with general free energy,
  Multiscale Modelling and Simulations 18, 502–541, 2020.  Supplementary Material: Movies and Simulations.
• J. A. Carrillo, Y.-P. Choi, Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces, Ann. IHP 37, 925–954, 2020.
• P. Aceves-Sánchez, M. Bostan, J. A. Carrillo, P. Degond, Hydrodynamic limits for kinetic flocking models of Cucker-Smale type, Math. Bio. Eng. 16, 7883-7910, 2019.
• J. A. Carrillo, Y.-P. Choi, O. Tse, Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces, Comm. Math. Phys. 365, 329-361, 2019.
• J. A. Carrillo, A. Wróblewska-Kaminska, E. Zatorska, On long-time asymptotics for viscous hydrodynamic models of collective behavior with damping and nonlocal interactions, Mathematical Models and Methods in the Applied Sciences 29, 31-63, 2019.
• J. A. Carrillo, Y.-P. Choi, S. Pérez, A review on attractive-repulsive hydrodynamics for consensus in collective behavior, in N. Bellomo, P. Degond, and E. Tadmor (Eds.), Active Particles Vol. I: Advances in Theory, Models, and Applications, Series: Modelling and Simulation in Science and Technology, Birkhäuser Basel, 259-298, 2017.
• M. Bostan, J. A. Carrillo, Reduced fluid models for self-propelled particles interacting through alignment, Mathematical Models and Methods in the Applied Sciences 27, 1255-1299, 2017.
• J. A. Carrillo, Y.-P. Choi, E. Zatorska, On the pressureless damped Euler-Poisson equations with non-local forces: Critical thresholds and large-time behavior, Mathematical Models and Methods in the Applied Sciences 26, 2311-2340, 2016.
• J. A. Carrillo, E. Feireisl, P. Gwiazda, A. Świerczewska-Gwiazda,Weak solutions for Euler systems with non-local interactions, J. Lond. Math. Soc. 95, 705-724, 2017.
• J. A. Carrillo, Y.-P. Choi, E. Tadmor, C. Tan, Critical thresholds in 1D Euler equations with nonlocal forces, Mathematical Models and Methods in the Applied Sciences 26, 185-206, 2016.

PDE Models in Population Dynamics

• S. Abo, J. A. Carrillo, A. T. Layton, Can the clocks tick together despite the noise? Stochastic simulations and analysis, to appear in SIAM J. Appl Dyn. Systems.
• F. Alvarez, J. A. Carrillo, J. Clairambault, Evolution of a structured cell population endowed with plasticity of traits under constraints on and between the traits, J. Math. Biology 85, Article n. 42, 2022.
• J. A. Carrillo, P. Gwiazda, K, Kropielnicka, A. Marciniak-Czochra, The Escalator Boxcar Train Method for a System of Aged-structured Equations in the Space of Measures, SIAM J. Numer. Anal. 57, 1842-1874, 2019.
• J. A. Cañizo, J. A. Carrillo, M. Pájaro, Exponential equilibration of genetic circuits using entropy methods, J. Math. Biology 78, 373–411, 2019.
• M. Pájaro, A. A. Alonso, J. A. Carrillo, C. Vázquez, Stability of stochastic gene regulatory networks using entropy methods, 2th IFAC Workshop on Thermodynamic Foundations for a Mathematical Systems Theory TFMST 2016 — Vigo, Spain, 28—30 September 2016, IFAC-PapersOnLine 49, 1–5, 2016.
• J. A. Carrillo, S. Martin, M.-T. Wolfram, A local version of the Hughes model for pedestrian flow, Mathematical Models and Methods in the Applied Sciences 26, 671–697, 2016.
• J. A. Carrillo, P. Gwiazda, A. Ulikowska, Splitting-Particle Methods for Structured Population Models: Convergence and Applications, Mathematical Models and Methods in the Applied Sciences 24, 2171, 2014. 
• J. A. Cañizo, J. A. Carrillo, S. Cuadrado, Measure solutions for some models in population dynamics, Acta Applicandae Mathematicae 123, 141-156, 2013.
• J. A. Carrillo, R. M. Colombo, P. Gwiazda, A. Ulikowska, Structured populations, cell growth and measure valued balance laws, J. Diff. Eqns. 252, 3245-3277, 2012.
• J.A. Carrillo, S. Cuadrado, B. Perthame, Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model, Mathematical Biosciences 205, 137-161, 2007.

PDE Models in Computational Neuroscience

• J. A. Carrillo, P. Roux, S. Solem, Noise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields, Physica D: Nonlinear Phenomena 449, 133736, 2023.
• J. A. Carrillo, X. Dou, Z. Zhou, A simplified voltage-conductance kinetic model for interacting neurons and its asymptotic limit, Preprint.
• J. A. Carrillo, A. Clini, S. Solem, The mean field limit of stochastic differential equation systems modelling grid cells, to appear in SIAM J. Math. Anal.
• J. A. Carrillo, H. Holden, S. Solem, Noise-driven bifurcations in a neural field system modelling networks of grid cells, J. Math. Biology 85, Article n. 42, 2022.
• J. A. Carrillo, B. Perthame, D. Salort, D. Smets, Qualitative Properties of Solutions for the Noisy Integrate & Fire model in Computational Neuroscience, Nonlinearity 28, 3365-3388, 2015.
• J. A. Carrillo, S. Mancini, M. B. Tran, On the exponential convergence rate for a non-gradient Fokker-Planck equation in Computational Neuroscience, JEPE 1, 271-279, 2015.
• J. A. Carrillo, S. Cordier, G. Deco, S. Mancini, Complexity Reduction of Rate-Equations Models for Two-Choice Decision-Making, PLoS ONE 8(12), e80820, 2013.
• J. A. Carrillo, S. Cordier, S. Mancini, One dimensional Fokker-Planck reduced dynamics of decision making models in Computational Neuroscience, Communications in Mathematical Sciences 11, 523–540, 2013.
• J. A. Carrillo, M. d. M. González, M. P. Gualdani, and M. E. Schonbek, Classical Solutions for a nonlinear Fokker-Planck equation arising in Computational Neuroscience, Comm. in PDEs 38, 385-409, 2013.
• M. J. Cáceres, J. A. Carrillo, B. Perthame, Analysis of Nonlinear Noisy Integrate & Fire Neuron Models: blow-up and steady states, Journal of Mathematical Neuroscience 1, 7, 2011.
• J. A. Carrillo, M. J. Cáceres, L. Tao, A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics, J. Comp. Phys. 230, 1084-1099, 2011.
• J. A. Carrillo, S. Cordier, S. Mancini, A decision-making Fokker-Planck model in Computational Neuroscience, J. Math. Biology 63, 801-830, 2011.

Nonlinear Diffusions: Entropy/Entropy Dissipation

• J. A. Cañizo, J. A. Carrillo, P. Laurençot, J. Rosado, The Fokker-Planck equation for bosons in 2D: well-posedness and asymptotic behavior, Nonlinear Analysis: TMA 137, 291-305, 2016.
• J. A. Carrillo, Y. Huang, M. C. Santos, J. L. Vázquez, Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure, J. Differential Equations 258, 736–763, 2015.
• J. A. Carrillo, G. Toscani, Renyi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations, Nonlinearity 27, 3159–3177, 2014.
• F. Bolley, J. A. Carrillo, Nonlinear diffusion: Geodesic Convexity is equivalent to Wasserstein Contraction, Comm. PDEs 39, 1860–1869, 2014.
• J.A. Carrillo, V. Caselles, S. Moll, On the relativistic heat equation in one space dimension, Proc. London Math. Soc. 107, 1395-1423, 2013.
• J. A. Cañizo, J. A. Carrillo, M. E. Schonbek, Decay rates for a class of diffusive-dominated interaction equations, J. Math. Anal. Appl. 389, 541-557, 2012.
• J. A. Carrillo, S. Lisini, On the asymptotic behavior of the gradient flow of a polyconvex functional, Contemporary Mathematics series 526, 37-51, 2010.
• M. Agueh, A. Blanchet, J. A. Carrillo, Large time asymptotics of the doubly nonlinear equation in the non-displacement convexity regime, J. Evol. Equations 10, 59-84, 2010.
• J. A. Carrillo, S. Lisini, G. Savare, D. Slepcev, Nonlinear mobility continuity equations and generalized displacement convexity, J. Functional Anal. 258, 1273-1309, 2010.
• J. A. Carrillo, D. Slepcev, Example of a displacement convex functional of first order, Calculus of Variations and PDES 36, 547-564, 2009.
• J. A. Carrillo, P. Laurençot, J. Rosado, Fermi-Dirac-Fokker-Planck Equation: Well-posedness & Long-time Asymptotics, J. Differential Equations 247, 2209-2234, 2009.
• J. A. Carrillo, M. P. Gualdani, A. Jüngel, Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in Rd, Pub. Mat. 52, 413-433, 2008.
• A. Arnold, J. A. Carrillo, C. Klapproth, Improved entropy decay estimates for the heat equation, J. Mathematical Analysis and Applications 343, 190-206, 2008.
• J.A. Carrillo, J. L. Vázquez, Asymptotic Complexity in Filtration Equations, Journal of Evolution Equations 7, 471-495, 2007.
• J.A. Carrillo, J. Rosado, F. Salvarani, 1D Nonlinear Fokker-Planck equations for Fermions and Bosons, Applied Mathematics Letters 21, 148-154, 2008.
• J.A. Carrillo, J. Dolbeault, I. Gentil, A. Jüngel, Entropy-Energy inequalities and improved convergence rates for nonlinear parabolic equations, Discrete Cont. Dynamical Systems B 6, 1027-1050, 2006.
• J.A. Carrillo, M. DiFrancesco, G. Toscani, Strict Contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering, Proc. Amer. Math. Soc. 135, 353-363, 2007.
• J.A. Carrillo, M. DiFrancesco, M. P. Gualdani, Semidiscretization and long-time asymptotics of nonlinear diffusion equations, Comm. Math. Sci. 1, Supplemental issue, 21-53, 2007.
• J.A. Carrillo, M. DiFrancesco, G. Toscani, Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for u_t=\Delta \phi(u), Archive for Rational Mechanics and Analysis 180, 127-149, 2006.
• J.A. Carrillo, G. Toscani, Wasserstein metric and large–time asymptotics of nonlinear diffusion equations, New Trends in Mathematical Physics, (In Honour of the Salvatore Rionero 70th Birthday), 234-244, 2005.
• J.A. Carrillo, EDPs de difusión y transporte óptimo de masa, Bol. Soc. Mat. Apl. 28, 129-154, 2004.
• J.A. Carrillo, K. Fellner, Long-time Asymptotics via Entropy Methods for Diffusion Dominated Equations, Asymptotic Analysis 42, 29-54, 2005.
• J.A. Carrillo, M. P. Gualdani, G. Toscani, Finite speed of propagation in porous media by mass transportation methods, C. R. Acad. Sci. Paris Ser. I 338, 815-818, 2004.
• J. A. Carrillo, C. Lederman, P.A. Markowich, G. Toscani, Poincaré Inequalities for Linearization of Very Fast Diffusion Equations, Nonlinearity 15, 565-580, 2002.
• J. A. Carrillo, G. Toscani, Intermediate asymptotics for strong solutions of the thin film equation, Comm. Math. Phys. 225, 551-571, 2002.
• J. A. Carrillo, A. Jungel, P.A. Markowich, G. Toscani, A.Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatshefte fur Mathematik, 133, 1-82, 2001.
• J. A. Carrillo, P.A. Markowich, A.Unterreiter, Large-Time Asymptotics of Porous-Medium Type Equations, Gakuto International Series Mathematical Sciences and Applications 13, 24-36, 2000.
• J. A. Carrillo, G. Toscani, Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity, Indiana University Mathematics Journal, 49,  113-141, 2000.
• J. A. Carrillo, G. Toscani, Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations, Math. Meth. Appl. Sci., 21, 1269-1286, 1998.

Kinetic Equations: Granular Media

• J. A. Carrillo, J. Hu, Z. Ma, T. Rey, Recent development in kinetic theory of granular materials: analysis and numerical methods, in: Albi G., Merino-Aceituno S., Nota A., Zanella M. (eds) Trails in Kinetic Theory. SEMA SIMAI Springer Series, vol 25. Springer, Cham., 2021.
• L. Almazán, J. A. Carrillo, C. Salueña, V. Garzó, T. Pöschel, Role of kinetic transport coefficients for hydrodynamic simulations of granular flow, New J. Phys. 15, 043044, 2013.
• L. Almazán, C. Salueña, V. Garzó, J. A. Carrillo, T. Pöschel, Hydrodynamics at the Navier-Stokes level applied to fast, transient, supersonic granular flows, AIP Conf. Proc. 1501, 993-1000, 2012.
• M. Bisi, J. A. Carrillo, B. Lods, Equilibrium solution to the inelastic Boltzmann equation driven by a particles thermal bath, J. Stat. Phys. 133, 841- 870, 2008.
• E. A. Carlen, J. A. Carrillo, M. C. Carvalho, Strong convergence towards homogeneous cooling states for dissipative Maxwell models, Annales de l’IHP-ANL 26, 1675-1700, 2009.
• J.A. Carrillo, S. Cordier, G. Toscani, Over-populated Tails for conservative-in-the-mean Inelastic Maxwell Models, Discrete and Continuous Dynamical Systems A 24, 59–81, 2009.
• J. A. Carrillo, G. Toscani, Contractive Probability Metrics and Asymptotic Behavior of Dissipative Kinetic Equations, Notes of the 2006 Porto Ercole Summer School, Rivista Matemàtica di Parma 6, 75-198, 2007.
• J. A. Carrillo, T. Pöschel, C. Salueña, Granular Hydrodynamics and Pattern Formation in Vertically Oscillated Granular Disks Layers, J. Fluid Mechanics 597, 119-144, 2008.
• F. Bolley, J.A. Carrillo, Tanaka Theorem for Inelastic Maxwell Models, Comm. Math. Phys. 276, 287-314, 2007.
• M. Bisi, J.A. Carrillo, G. Toscani, Decay rates in probability metrics towards homogeneous cooling states for the inelastic Maxwell model, J. Stat. Phys. 124, 625-653, 2006.
• J. A. Carrillo, C. Salueña, Modelling of Shock Waves and Clustering in Hydrodynamic Simulations of Granular Gases, Modelling and Numerics of Kinetic Dissipative Systems, 175-189, Nova Science Publishers NY, 2006.
• C. Salueña, J. A. Carrillo, Numerical simulation of hydrodynamic equations for granular media, Powders & Grains 2005: Garcia-Rojo, Hermann and McNamara eds. pp 481-484. A.A. Balkema, London (2005)
• M. Bisi, J.A. Carrillo, G. Toscani, Contractive Metrics for a Boltzmann equation for granular gases: Diffusive equilibria, J. Stat. Phys. 118, 301-331, 2005.
• J.A. Carrillo, R.J. McCann, C. Villani, Contractions in the 2-Wasserstein length space and thermalization of granular media, Archive for Rational Mechanics and Analysis 179, 217-263, 2006.
• J.A. Carrillo, R.J. McCann, C. Villani, Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Revista Matemática Iberoamericana 19, 1-48, 2003.
• J. A. Carrillo, C. Cercignani, I. Gamba, Steady states of a Boltzmann equation for driven granular media, Phys. Rev. E., 62, 7700-7707, 2000.
• A. V. Bobylev, J. A. Carrillo, I. Gamba, On some properties of kinetic and hydrodynamic equations for inelastic interactions, J. Stat. Phys., 98, 743-773, 2000.
• J. A. Carrillo, On a 1-D granular media immersed in a fluid, Fields Institute Communications, 27, 43-56, 2000.
• D. Benedetto, E. Caglioti, J. A. Carrillo, M. Pulvirenti, A non-maxwellian steady distribution for one-dimensional granular media, J. Stat. Phys., 91, 979-990, 1998.

Kinetic Equations: VPFP and related models

• J. A. Carrillo, Y.-P. Choi, Y. Peng, Large friction-high force fields limit for the nonlinear Vlasov-Poisson-Fokker-Planck system, Kinetic and Related Models 15, 355-384, 2022.
• J. A. Carrillo, L. Wang, W. Xu, M. Yan, Variational Asymptotic Preserving Scheme for the Vlasov-Poisson-Fokker-Planck System, Multiscale Model. Simul. 19, 478–505, 2021.
• J. A. Carrillo, Y.-P. Choi, S. Salem, Propagation of chaos for the VPFP equation with a polynomial cut-off, Commun. Contemp. Math. 21, 1850039, 2019.
• J. A. Carrillo, Y.-P. Choi, T. K. Karper, On the analysis of a coupled kinetic-fluid model with local alignment forces, Ann. IHP 33, 273-307, 2016.
• J. A. Carrillo, Y.-P. Choi, S.-Y. Ha, M.-J. Kang, Y. Kim, Contractivity of the Wasserstein metric for the kinetic Kuramoto equation, J. Stat. Phys. 156, 395–415, 2014.
• J. A. Carrillo, T. Karper, K. Trivisa, On the dynamics of a fluid-particle interaction model: The Bubbling Regime, Nonlinear Analysis TMA 74, 2778-2801, 2011.
• J. A. Carrillo, R. Duan, A. Moussa, Global Classical Solutions Close to Equilibrium to the Vlasov-Euler-Fokker-Planck System, Kinetic and Related Models 4, 227-258, 2011.
• M. Bisi, J. A. Carrillo, G. Spiga, Some alternative methods for hydrodynamic closures to dissipative kinetic models, Eur. Phys. J. Special Topics 179, 165-178, 2009.
• A. Arnold, J. A. Carrillo, C. Manzini, Refined long-time asymptotics for some polymeric fluid flow models, Comm. Math. Sci. 8, 763-782, 2010.
• J. A. Carrillo, L. Desvillettes, K. Fellner, Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion, Comm. in PDEs 34, 1338-1351, 2009.
• J.A. Carrillo, L. Desvillettes, K. Fellner, Fast-Reaction Limit for the Inhomogeneous Aizenman-Bak Model, Kinetic and Related Models 1, 127-137, 2008.
• J.A. Carrillo, L. Desvillettes, K. Fellner, Exponential Decay Towards Equilibrium for the Inhomogeneous Aizenman-Bak Model, Comm. Math. Phys. 278, 433-451, 2008.
• J.A. Carrillo, T. Goudon, Stability and Asymptotic Analysis of a Fluid-Particle Interaction Model, Comm. PDE 31, 1349 – 1379, 2006.
• J.A. Carrillo, S. Labrunie, Global solutions for the one-dimensional Vlasov-Maxwell system for Laser-plasma interaction, Math. Mod. Meth. Appl. Sci. 16, 19-57, 2006.
• A. Jungel, A. Arnold, J.A. Carrillo, L. Desvillettes, J. Dolbeault, C. Villani, G. Toscani, C. Lederman, P.A. Markowich, Entropies and equilibria of many-particle systems: An essay on recent research, Monat. Mathematik. 142, 35-43, 2004.
• A. Arnold, J. A. Carrillo, E. Dhamo, On the periodic Wigner-Poisson-Fokker-Planck system, Journal of Mathematical Analysis and Applications 275, 263-276, 2002.
• A. Arnold, J. A. Carrillo, M. Tidriri, Large-time behavior of discrete kinetic equations with non-symmetric interactions, Mathematical Models and Methods in the Applied Sciences 12, 1555-1564, 2002.
• M.J. Cáceres, J.A. Carrillo, T. Goudon, Equilibration rate for the linear inhomogeneous relaxation-time Boltzmann equation for charged particles, Comm. in PDE. 28, 969-989, 2003.
• M.J. Caceres, J.A. Carrillo, J. Dolbeault, Nonlinear stability in Lp for solutions of the Vlasov-Poisson system for charged particles, SIAM J. Math. Anal. 34, 478-494, 2002.
• A. Arnold, J. A. Carrillo, I. Gamba, C. Shu, Low and High Field Scaling Limits for the Vlasov- and Wigner-Poisson-Fokker-Planck Systems, Transp. Theory Stat. Phys., 30, 121-153, 2001.
• J.A. Carrillo, Global weak solutions for the initial-boundary value problems to the Vlasov-Poisson-Fokker-Planck system, Math. Meth. Appl. Sci., 21, 907-938, 1998.
• J.A. Carrillo, J. Soler, On functional solutions for the three dimensional kinetic equations of Vlasov-type with bounded measures as initial data, Nonlinear Analysis 32, 235-259, 1998.
• J.A. Carrillo, J. Soler, Functional solutions for the Vlasov-Poisson system, Appl. Math. Lett. 10, 45-50, 1997.
• J.A. Carrillo, J. Soler, On the Vlasov-Poisson-Fokker-Planck equations with measures in Morrey spaces as initial data, J. Math. Anal. Appl. 207, 475-495, 1997.
• L.L. Bonilla, J.A. Carrillo, J. Soler, Asymptotic behaviour of the initial boundary value problem for the three-dimensional Vlasov-Poisson-Fokker-Planck system, SIAM J. Appl. Math. 57, 1343-1372, 1997.
• L.L. Bonilla, J.A. Carrillo, J. Soler, An H-theorem for electrostatic and self-gravitating Vlasov-Poisson- Fokker-Planck systems, Physics Letters A 212, 55-59, 1996.
• J.A. Carrillo, J. Soler, J.L. Vázquez, Asymptotic behaviour and selfsimilarity for the three dimensional Vlasov-Poisson-Fokker-Planck system, J. Functional Analysis 141, 99-132, 1996.
• J.A. Carrillo, J. Soler, On the initial value problem for the Vlasov-Poisson- Fokker-Planck system with initial data in Lp-spaces, Math. Meth. Appl. Sci. 18, 825-839, 1995.
• J.A. Carrillo, J. Soler, J.L. Vázquez, Asymptotic behaviour for the frictionless Vlasov-Poisson-Fokker-Planck system, C.R. Acad. Sci. Paris 321, 1195-1200, 1995.
• L.L. Bonilla, J.A. Carrillo, J. Soler, Asymptotic behavior of the Vlasov-Poisson-Fokker-Planck system in bounded domains, Z. Angew. Math. Mech. 76, 485-486, 1996.
• J.A. Carrillo, J. Soler, Global existence of functional solutions for the Vlasov-Poisson- Fokker-Planck system in 3-D with bounded measures as initial data, Pitman Research Notes in Mathematics, 326, 1994.

Kinetic Equations: Semiconductors

• N. Ben Abdallah, M. J. Cáceres, J. A. Carrillo, F. Vecil, A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs, J. Comp. Phys. 228, 6553-6571, 2009.
• J.A. Carrillo, A. Majorana, F. Vecil, A Semi-lagrangian deterministic solver for the semiconductor Boltzmann-Poisson system, Commun. Comput. Phys. 2, 1027-1054, 2007.
• M.J. Cáceres, J. A. Carrillo, I. Gamba, A. Majorana, C. W. Shu, DSMC versus WENO-BTE: A double gate MOSFET example, Journal of Computational Electronics 5, 471-474, 2006.
• M.J. Cáceres, J. A. Carrillo, I. Gamba, A. Majorana, C. W. Shu, Deterministic kinetic solvers for charged particle transport in semiconductor devices, in Cercignani, C., Gabetta, E. (eds.) Transport Phenomena and Kinetic Theory: Applications to Gases, Semiconductors, Photons and Biological Systems, Series: Modelling and Simulation in Science and Technology, Birkhäuser, 151-171.
• M.J. Cáceres, J.A. Carrillo, A. Majorana, Deterministic simulation of the Boltzmann-Poisson system in GaAs-based semiconductors, SIAM Journal of Scientific Computing 27, 1981-2009, 2006.
• J. M. Mantas, J. A. Carrillo, A. Majorana, Parallelization of WENO-Boltzmann schemes for kinetic descriptions of 2D semiconductor devices, in Anile, A.M., Ali, G.; Mascali, G. (eds.) Scientific Computing in Electrical Engineering, Series: Mathematics in Industry Subseries: The European Consortium for Mathematics in Industry , Vol. 9 Springer, Berlin, (2006), 357-362.
• P. González, J. A. Carrillo, F. Gámiz, Deterministic Numerical Simulation of 1d kinetic descriptions of Bipolar Electron Devices, in Anile, A.M., Ali, G.; Mascali, G. (eds.) Scientific Computing in Electrical Engineering, Series: Mathematics in Industry Subseries: The European Consortium for Mathematics in Industry , Vol. 9 Springer, Berlin, (2006), 339-344.
• J. A. Carrillo, I. Gamba, A. Majorana, C. W. Shu, 2D semiconductor device simulations by WENO-Boltzmann schemes: efficiency, boundary conditions and comparison to Monte Carlo methods, Journal of Computational Physics 214, 55-80, 2006.
• P. González, A. Godoy, F. Gámiz, J. A. Carrillo, Accurate Deterministic Numerical Simulation of p-n Junctions, Journal of Computational Electronics 3, 235-238, 2004.
• J. A. Carrillo, I. M. Gamba, A. Majorana, C.W. Shu,  A direct solver for 2D non-stationary Boltzmann-Poisson Systems for Semiconductor Devices: A MESFET simulation by WENO-Boltzmann schemes, Journal of Computational Electronics 2, 375-380, 2003.
• J. A. Carrillo, I. M. Gamba, A. Majorana, C.W. Shu,  A WENO-solver for the 1D non-stationary Boltzmann-Poisson system for semiconductor devices, Journal of Computational Electronics 1, 365-370, 2002.
• J. A. Carrillo, I. M. Gamba, O. Muscato, C.W.Shu, Comparison of Monte Carlo and deterministic simulations of a silicon diode, IMA Volume Series 135, 75-84, 2003.
• A. M. Anile, J.A. Carrillo, I. M. Gamba, C.W. Shu, Approximation of the BTE by a relaxation-time operator: simulations for a 50nm-channel Si diode, VLSI design Journal 13, 349-354, 2001.
• J. A. Carrillo, I. Gamba, C. W. Shu, Computational macroscopic approximations to the 1-D relaxation-time kinetic system for semiconductors, Physica D, 146, 289-306, 2000.

Kinetic Equations:  Numerical Analysis, Scientific Computing and Modelling

• R. Bailo, J. A. Carrillo, S. Kalliadasis, S. P. Perez, Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation, Preprint.
• J. A. Carrillo, M. Parisot, Z. Szymańska, Mathematical Modelling of Collagen Fibers Rearrangement During Tendon Healing Process, Kinetic and Related Models 14, 283-301, 2021.
• N. Kruk, J. A. Carrillo, H. Koeppel, A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles, J. Comp. Phys. 440, 110275, 2021. Supplementary Material: Movies and Simulations.
• J. A. Carrillo, S. Kalliadasis, F. Liang, S. P. Perez, Enhancement of damaged-image prediction through Cahn-Hilliard Image Inpainting, R. Soc. Open Sci. 8, 201294, 2021.
• N. Kruk, J. A. Carrillo, H. Koeppel, Traveling Bands, Clouds, and Vortices of Chiral Active Matter, Physical Review E 102, 022604, 2020. Supplementary Material: Movies and Simulations.
• V. Bonnaillie-Noël, J.A. Carrillo, T. Goudon, G. Pavliotis, Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations, IMA Journal of Numerical Analysis 36,1536-1569, 2016.
• J. A. Carrillo, B. Yan, An Asymptotic Preserving Scheme for the Diffusive Limit of Kinetic systems for Chemotaxis, Multiscale Model. Simul. 11, 336–361, 2013.
• B. Ayuso de Dios, J. A. Carrillo, C.-W. Shu, Discontinuous Galerkin methods for the multi-dimensional Vlasov-Poisson problem, Math. Mod. Meth. Appl Sci. 22, 1250042, 2012.
• B. Ayuso, J. A. Carrillo, C.-W. Shu, Discontinuous Galerkin Methods for the one-dimensional Vlasov-Poisson System, Kinetic and Related Models 4, 955 – 989, 2011.
• J.A. Carrillo, T. Goudon, P. Lafitte, Simulation of Fluid & Particles Flows: Asymptotic Preserving Schemes for Bubbling and Flowing Regimes, J. Comp. Phys. 227, 7929-7951, 2008.
• Y. Hyon, J. A. Carrillo, Q. Du, C. Liu, A Macroscopic Closure Approximation to the Micro-Macro FENE Models with Maximum Entropy Principle for Polymeric Materials, Kinetic and Related Models 1, 171-184, 2008.
• J.A. Carrillo, T. Goudon, P. Lafitte, F. Vecil, Numerical Schemes of Diffusion Asymptotics and Moment Closures for Kinetic Equations, J. Sci. Comp. 35, 113-149, 2008.
• J. M. Mantas, P. González, J. A. Carrillo, Parallelization of Implicit-Explicit Runge-Kutta Methods for Cluster of PCs, Proceedings of the Euro-Par 2005 Parallel Processing: 11th International Euro-Par Conference, Editors: José C. Cunha, Pedro D. Medeiros, pp 815-825, Lecture Notes in Computer Science 3648, Springer-Verlag 2005.
• J. M. Mantas-Ruiz, L. Pareschi, J. A. Carrillo, J. Ortega-Lopera, Parallel Integration of Hydrodynamical Approximations of the Boltzmann Equation for rarefied gases on a Cluster of Computers, J. of Computational Methods in Science and Engineering 4, 33-41, 2004.
• J.A. Carrillo, T. Goudon, A numerical study on large-time asymptotics of the Lifshitz-Slyozov system, Journal of Scientific Computing 20, 69-113, 2004.
• J. M. Mantas-Ruiz, J. Ortega-Lopera, J. A. Carrillo, Component-based derivation of a parallel stiff ODE solver implemented in a cluster of computers, International Journal of Paralell Programing,  30, 99-148, 2002.

Other Nonlinear PDEs: Analysis

• J. A. Carrillo, K. Grunert, H. Holden, A Lipschitz metric for the Camassa-Holm equation, Forum of Mathematics, Sigma 8, e27, 2020.
• J. A. Carrillo, K. Grunert, H. Holden, A Lipschitz metric for the Hunter-Saxton equation, Comm. PDE 44, 309-334, 2019.
• J. A. Carrillo, L. Ni, Sharp logarithmic Sobolev inequalities on gradient solitons and applications, Communications in Analysis and Geometry 17, 721-753, 2009.
• M. Bostan, J. A. Carrillo, Global solutions for the one dimensional Water Bag model, Comm. Math. Sci 7, 129-141, 2009.
• J.A. Carrillo, M. Di Francesco, C. Lattanzio, Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws, Bollettino UMI 10-B, 277-292, 2007.
• J.A. Carrillo, L.C.F. Ferreira, Asymptotic Behavior for the Sub-critical Dissipative Quasi-Geostrophic Equations, Nonlinearity 21, 1001-1018, 2008.
• J.A. Carrillo, L.C.F. Ferreira, Convergence towards Self-similar Asymptotic Behavior for the Dissipative Quasi-Geostrophic Equations, Banach Center Publ. 74, 95-115, 2006.
• J.A. Carrillo, M. Di Francesco, C. Lattanzio, Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws, J. Diff. Equations 231, 425-458, 2006.
• J.A. Carrillo, L.C.F. Ferreira, Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equations, Monatshefte für Mathematik 151, 111-142, 2007.
• J. A. Carrillo, J. Soler, On the evolution of an angle in a vortex patch, J. Nonlinear Sci., 10, 23-47, 2000.
• J. A. Carrillo, J. Soler, On the evolution of a singular vortex patch in a two-dimensional incompressible fluid flow, Computer Physics Communications, 121-122, 244-250, 1999.
• J.A. Carrillo, On a non-local elliptic equation with decreasing nonlinearity arising in plasma physics, Nonlinear Analysis 32, 97-115, 1998.