Imperial College London

ProfessorJose AntonioCarrillo de la Plata

Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied and Numerical Analysis



+44 (0)20 7594 8530carrillo Website CV




6M26Huxley BuildingSouth Kensington Campus





José A. Carrillo currently holds a Chair in Applied and Numerical Analysis at Imperial College London appointed in October 2012. He was formerly  ICREA Research Professor at the Universitat Autònoma de Barcelona during the period 2003-2012. He was a lecturer at the University of Texas at Austin 1998-2000. He held assistant and associate professor positions at the Universidad de Granada 1992-1998 and 2000-2003, where he also did his PhD. He served as chair of the Applied Mathematics Committee of the European Mathematical Society 2014-2017. He was the chair of the 2018 Year of Mathematical Biology. He has been elected as member of the European Academy of Sciences, Section Mathematics, in 2018. He is currently the Program Director of the SIAM activity group in Analysis of PDE.

His research field is Partial Differential Equations (PDEs). They constitute the basic language in which most of the laws in physics or engineering can be written and one of the most important mathematical tools for modelling in life and socio-economical sciences. The modelling based on PDEs, their mathematical analysis, the numerical schemes, and their simulation in applications are his general topics of research. His expertise comprises long-time asymptotics, qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations in the modelling of collective behaviour of many-body systems such as rarefied gases, granular media, charge particle transport in semiconductors, or cell movement by chemotaxis. He was recognised with the SEMA prize (2003) and the GAMM Richard Von-Mises prize (2006) for young researchers. He was a recipient of a Wolfson Research Merit Award by the Royal Society 2012-2017. He was awarded the 2016 SACA award for best PhD supervision at Imperial College London.

Selected Publications

Journal Articles

Carrillo JA, Choi Y-P, Tse O, 2019, Convergence to Equilibrium in Wasserstein Distance for Damped Euler Equations with Interaction Forces, Communications in Mathematical Physics, Vol:365, ISSN:0010-3616, Pages:329-361

Carrillo J-A, Santambrogio F, 2018, L-infinity estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems, Quarterly of Applied Mathematics, Vol:76, ISSN:0033-569X, Pages:515-530

Cañizo JA, Carrillo JA, Pájaro M, 2018, Exponential equilibration of genetic circuits using entropy methods., J Math Biol

Pinto MC, Carrillo JA, Charles F, et al., 2018, Convergence of a linearly transformed particle method for aggregation equations, Numerische Mathematik, Vol:139, ISSN:0029-599X, Pages:743-793

Carrillo JA, Choi Y-P, Totzeck C, et al., 2018, An analytical framework for consensus-based global optimization method, Mathematical Models & Methods in Applied Sciences, Vol:28, ISSN:0218-2025, Pages:1037-1066

Carrillo JA, During B, Matthes D, et al., 2018, A Lagrangian Scheme for the Solution of Nonlinear Diffusion Equations Using Moving Simplex Meshes, Journal of Scientific Computing, Vol:75, ISSN:0885-7474, Pages:1463-1499

Carrillo JA, Colombi A, Scianna M, 2018, Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles, Journal of Theoretical Biology, Vol:445, ISSN:0022-5193, Pages:75-91

Barre J, Carrillo JA, Degond P, et al., 2018, Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions, Journal of Nonlinear Science, Vol:28, ISSN:0938-8974, Pages:235-268

CARRILLO JA, JÜNGEL A, SANTOS MC, 2018, Displacement convexity for the entropy in semi-discrete non-linear Fokker–Planck equations†, European Journal of Applied Mathematics, ISSN:0956-7925, Pages:1-20

Carrillo JA, Huang Y, Schmidtchen M, 2018, ZOOLOGY OF A NONLOCAL CROSS-DIFFUSION MODEL FOR TWO SPECIES, SIAM Journal on Applied Mathematics, Vol:78, ISSN:0036-1399, Pages:1078-1104

Bailo R, Bongini M, Carrillo JA, et al., 2018, Optimal consensus control of the Cucker-Smale model, Ifac Papersonline, Vol:51, ISSN:2405-8963, Pages:1-6

Sun Z, Carrillo JA, Shu C-W, 2018, A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials, Journal of Computational Physics, Vol:352, ISSN:0021-9991, Pages:76-104

Carrillo JA, Choi Y-P, Mucha PB, et al., 2017, Sharp conditions to avoid collisions in singular Cucker-Smale interactions, Nonlinear Analysis-Real World Applications, Vol:37, ISSN:1468-1218, Pages:317-328

Carrillo JA, Figalli A, Patacchini FS, 2017, Geometry of minimizers for the interaction energy with mildly repulsive potentials, Annales de l Institut Henri Poincare-Analyse Non Lineaire, Vol:34, ISSN:0294-1449, Pages:1299-1308

Carrillo JA, Huang Y, Patacchini FS, et al., 2017, NUMERICAL STUDY OF A PARTICLE METHOD FOR GRADIENT FLOWS, Kinetic and Related Models, Vol:10, ISSN:1937-5093, Pages:613-641

Calvez V, Carrillo JA, Hoffmann F, 2017, Equilibria of homogeneous functionals in the fair-competition regime, Nonlinear Analysis-Theory Methods & Applications, Vol:159, ISSN:0362-546X, Pages:85-128

Bostan M, Carrillo JA, 2017, Reduced fluid models for self-propelled particles interacting through alignment, Mathematical Models & Methods in Applied Sciences, Vol:27, ISSN:0218-2025, Pages:1255-1299

Carrillo JA, Feireisl E, Gwiazda P, et al., 2017, Weak solutions for Euler systems with non-local interactions, Journal of the London Mathematical Society - Second Series, Vol:95, ISSN:0024-6107, Pages:705-724

Carrillo JA, Huang Y, 2017, EXPLICIT EQUILIBRIUM SOLUTIONS FOR THE AGGREGATION EQUATION WITH POWER-LAW POTENTIALS, Kinetic and Related Models, Vol:10, ISSN:1937-5093, Pages:171-192

Carrillo JA, Ranetbauer H, Wolfram M-T, 2016, Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms, Journal of Computational Physics, Vol:327, ISSN:0021-9991, Pages:186-202

Bonnaillie-Noel V, Carrillo JA, Goudon T, et al., 2016, Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations, IMA Journal of Numerical Analysis, Vol:36, ISSN:0272-4979, Pages:1536-1569

Canizo JA, Carrillo JA, Laurencot P, et al., 2016, The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior, Nonlinear Analysis-Theory Methods & Applications, Vol:137, ISSN:0362-546X, Pages:291-305

Carrillo JA, Delgadino MG, Mellet A, 2016, Regularity of Local Minimizers of the Interaction Energy Via Obstacle Problems, Communications in Mathematical Physics, Vol:343, ISSN:0010-3616, Pages:747-781

Carrillo JA, Martin S, Wolfram M-T, 2016, An improved version of the Hughes model for pedestrian flow, Mathematical Models & Methods in Applied Sciences, Vol:26, ISSN:0218-2025, Pages:671-697

Carrillo JA, Slepcev D, Wu L, 2016, NONLOCAL-INTERACTION EQUATIONS ON UNIFORMLY PROX-REGULAR SETS, Discrete and Continuous Dynamical Systems, Vol:36, ISSN:1078-0947, Pages:1209-1247

Carrillo JA, James F, Lagoutiere F, et al., 2016, The Filippov characteristic flow for the aggregation equation with mildly singular potentials, Journal of Differential Equations, Vol:260, ISSN:0022-0396, Pages:304-338

Carrillo JA, Choi Y-P, Tadmor E, et al., 2016, Critical thresholds in 1D Euler equations with non-local forces, Mathematical Models & Methods in Applied Sciences, Vol:26, ISSN:0218-2025

Carrillo JA, Di Francesco M, Toscani G, 2016, Condensation phenomena in nonlinear drift equations, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, Vol:15, ISSN:0391-173X, Pages:145-171

Carrillo JA, Patacchini FS, Sternberg P, et al., 2016, CONVERGENCE OF A PARTICLE METHOD FOR DIFFUSIVE GRADIENT FLOWS IN ONE DIMENSION, SIAM Journal on Mathematical Analysis, Vol:48, ISSN:0036-1410, Pages:3708-3741

Carrillo JA, Klar A, Roth A, 2016, SINGLE TO DOUBLE MILL SMALL NOISE TRANSITION VIA SEMI-LAGRANGIAN FINITE VOLUME METHODS, Communications in Mathematical Sciences, Vol:14, ISSN:1539-6746, Pages:1111-1136

Barbaro ABT, Canizo JA, Carrillo JA, et al., 2016, PHASE TRANSITIONS IN A KINETIC FLOCKING MODEL OF CUCKER-SMALE TYPE, Multiscale Modeling & Simulation, Vol:14, ISSN:1540-3459, Pages:1063-1088

Blanchet A, Carrillo JA, Kinderlehrer D, et al., 2015, A HYBRID VARIATIONAL PRINCIPLE FOR THE KELLER-SEGEL SYSTEM IN R-2, Mathematical Modelling and Numerical Analysis - Modelisation Mathematique et Analyse Numerique, Vol:49, ISSN:0764-583X, Pages:1553-1576

Carrillo JA, Mancini S, Tran M-B, 2015, ON THE EXPONENTIAL CONVERGENCE RATE FOR A NON-GRADIENT FOKKER-PLANCK EQUATION IN COMPUTATIONAL NEUROSCIENCE, Journal of Elliptic and Parabolic Equations, Vol:1, ISSN:2296-9020, Pages:271-279

Carrillo JA, Luis Vazquez J, 2015, Some free boundary problems involving non-local diffusion and aggregation, Royal Society of London. Philosophical Transactions A. Mathematical, Physical and Engineering Sciences, Vol:373, ISSN:1364-503X

Canizo JA, Carrillo JA, Patacchini FS, 2015, Existence of Compactly Supported Global Minimisers for the Interaction Energy, Archive for Rational Mechanics and Analysis, Vol:217, ISSN:0003-9527, Pages:1197-1217

Carrillo JA, Eftimie R, Hoffmann F, 2015, NON-LOCAL KINETIC AND MACROSCOPIC MODELS FOR SELF-ORGANISED ANIMAL AGGREGATIONS, Kinetic and Related Models, Vol:8, ISSN:1937-5093, Pages:413-441

Carrillo JA, Perthame B, Salort D, et al., 2015, Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience, Nonlinearity, Vol:28, ISSN:0951-7715, Pages:3365-3388

Bonaschi GA, Carrillo JA, Di Francesco M, et al., 2015, EQUIVALENCE OF GRADIENT FLOWS AND ENTROPY SOLUTIONS FOR SINGULAR NONLOCAL INTERACTION EQUATIONS IN 1D, ESAIM-Control Optimisation and Calculus of Variations, Vol:21, ISSN:1292-8119, Pages:414-441

Carrillo JA, Huang Y, Santos MC, et al., 2015, Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure, Journal of Differential Equations, Vol:258, ISSN:0022-0396, Pages:736-763

Carrillo JA, Castorina D, Volzone B, 2015, GROUND STATES FOR DIFFUSION DOMINATED FREE ENERGIES WITH LOGARITHMIC INTERACTION, SIAM Journal on Mathematical Analysis, Vol:47, ISSN:0036-1410, Pages:1-25

Carrillo JA, Toscani G, 2014, Renyi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations, Nonlinearity, Vol:27, ISSN:0951-7715, Pages:3159-3177

Carrillo JA, Gwiazda P, Ulikowska A, 2014, Splitting-particle methods for structured population models: Convergence and applications, Mathematical Models & Methods in Applied Sciences, Vol:24, ISSN:0218-2025, Pages:2171-2197

Carrillo JA, Huang Y, Martin S, 2014, Nonlinear stability of flock solutions in second-order swarming models, Nonlinear Analysis-Real World Applications, Vol:17, ISSN:1468-1218, Pages:332-343

Carrillo JA, Lisini S, Mainini E, 2014, UNIQUENESS FOR KELLER-SEGEL-TYPE CHEMOTAXIS MODELS, Discrete and Continuous Dynamical Systems, Vol:34, ISSN:1078-0947, Pages:1319-1338

Albi G, Balague D, Carrillo JA, et al., 2014, STABILITY ANALYSIS OF FLOCK AND MILL RINGS FOR SECOND ORDER MODELS IN SWARMING, SIAM Journal on Applied Mathematics, Vol:74, ISSN:0036-1399, Pages:794-818

Carrillo JA, Cordier S, Deco G, et al., 2013, Complexity Reduction of Rate-Equations Models for Two-Choice Decision-Making, PLOS One, Vol:8, ISSN:1932-6203

Carrillo JA, Caselles V, Moll S, 2013, On the relativistic heat equation in one space dimension, Proceedings of the London Mathematical Society, Vol:107, ISSN:0024-6115, Pages:1395-1423

Bostan M, Carrillo JA, 2013, ASYMPTOTIC FIXED-SPEED REDUCED DYNAMICS FOR KINETIC EQUATIONS IN SWARMING, Mathematical Models & Methods in Applied Sciences, Vol:23, ISSN:0218-2025, Pages:2353-2393

Balague D, Carrillo JA, Laurent T, et al., 2013, Dimensionality of Local Minimizers of the Interaction Energy, Archive for Rational Mechanics and Analysis, Vol:209, ISSN:0003-9527, Pages:1055-1088

Almazan L, Carrillo JA, Saluena C, et al., 2013, A numerical study of the Navier-Stokes transport coefficients for two-dimensional granular hydrodynamics, New Journal of Physics, Vol:15, ISSN:1367-2630

Ayuso De Dios B, Carrillo JA, Shu C-W, 2012, DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV-POISSON PROBLEM, Mathematical Models & Methods in Applied Sciences, Vol:22, ISSN:0218-2025

Carrillo JA, Ferreira LCF, Precioso JC, 2012, A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity, Advances in Mathematics, Vol:231, ISSN:0001-8708, Pages:306-327

Blanchet A, Carlen EA, Carrillo JA, 2012, Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model, Journal of Functional Analysis, Vol:262, ISSN:0022-1236, Pages:2142-2230

Antonio Carrillo J, Cordier S, Mancini S, 2011, A decision-making Fokker-Planck model in computational neuroscience, Journal of Mathematical Biology, Vol:63, ISSN:0303-6812, Pages:801-830

Bolley F, Canizo JA, Carrillo JA, 2011, STOCHASTIC MEAN-FIELD LIMIT: NON-LIPSCHITZ FORCES AND SWARMING, Mathematical Models & Methods in Applied Sciences, Vol:21, ISSN:0218-2025, Pages:2179-2210

Carrillo JA, Difrancesco M, Figalli A, et al., 2011, GLOBAL-IN-TIME WEAK MEASURE SOLUTIONS AND FINITE-TIME AGGREGATION FOR NONLOCAL INTERACTION EQUATIONS, Duke Mathematical Journal, Vol:156, ISSN:0012-7094, Pages:229-271

Carlen EA, Carrillo JA, Loss M, 2010, Hardy-Littlewood-Sobolev inequalities via fast diffusion flows, Proceedings of the National Academy of Sciences of the United States of America, Vol:107, ISSN:0027-8424, Pages:19696-19701

Carrillo JA, Fornasier M, Rosado J, et al., 2010, ASYMPTOTIC FLOCKING DYNAMICS FOR THE KINETIC CUCKER-SMALE MODEL, SIAM Journal on Mathematical Analysis, Vol:42, ISSN:0036-1410, Pages:218-236

Ben Abdallah N, Caceres MJ, Carrillo JA, et al., 2009, A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs, Journal of Computational Physics, Vol:228, ISSN:0021-9991, Pages:6553-6571

Carrillo JA, D'Orsogna MR, Panferov V, 2009, DOUBLE MILLING IN SELF-PROPELLED SWARMS FROM KINETIC THEORY, Kinetic and Related Models, Vol:2, ISSN:1937-5093, Pages:363-378

Blanchet A, Carrillo JA, Laurencot P, 2009, Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions, Calculus of Variations and Partial Differential Equations, Vol:35, ISSN:0944-2669, Pages:133-168

Bertozzi AL, Carrillo JA, Laurent T, 2009, Blow-up in multidimensional aggregation equations with mildly singular interaction kernels, Nonlinearity, Vol:22, ISSN:0951-7715, Pages:683-710


Blanchet A, Carrillo JA, Masmoudi N, 2008, Infinite time aggregation for the critical Patlak-Keller-Segel model in R-2, Communications on Pure and Applied Mathematics, Vol:61, ISSN:0010-3640, Pages:1449-1481

Carrillo JA, Poschel T, Saluena C, 2008, Granular hydrodynamics and pattern formation in vertically oscillated granular disk layers, Journal of Fluid Mechanics, Vol:597, ISSN:0022-1120, Pages:119-144

Blanchet A, Calvez V, Carrillo JA, 2008, Convergence of the mass-transport steepest descent scheme for the subcritical Patlak-Keller-Segel model, SIAM Journal on Numerical Analysis, Vol:46, ISSN:0036-1429, Pages:691-721

Carrillo JA, Vecil F, 2007, Nonoscillatory interpolation methods applied to Vlasov-based models, SIAM Journal on Scientific Computing, Vol:29, ISSN:1064-8275, Pages:1179-1206

Calvez V, Carrillo JA, 2006, Volume effects in the Keller-Segel model: energy estimates preventing blow-up, Journal de Mathematiques Pures et Appliquees, Vol:86, ISSN:0021-7824, Pages:155-175

Carrillo JA, McCann RJ, Villani CD, 2006, Contractions in the 2-Wasserstein length space and thermalization of granular media, Archive for Rational Mechanics and Analysis, Vol:179, ISSN:0003-9527, Pages:217-263

Carrillo JA, McCann RJ, Villani C, 2003, Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Revista Matematica Iberoamericana, Vol:19, ISSN:0213-2230, Pages:971-1018

Carrillo JA, Vazquez JL, 2003, Fine asymptotics for fast diffusion equations, Communications in Partial Differential Equations, Vol:28, ISSN:0360-5302, Pages:1023-1056

Carrillo JA, Toscani G, 2002, Long-time asymptotics for strong solutions of the thin film equation, Communications in Mathematical Physics, Vol:225, ISSN:0010-3616, Pages:551-571

Carrillo JA, Jungel A, Markowich PA, et al., 2001, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatshefte fur Mathematik, Vol:133, ISSN:0026-9255, Pages:1-82

Carrillo JA, Toscani G, 2000, Asymptotic L-1-decay of solutions of the porous medium equations to self-similarity, Indiana University Mathematics Journal, Vol:49, ISSN:0022-2518, Pages:113-142

Bobylev AV, Carrillo JA, Gamba IM, 2000, On some properties of kinetic and hydrodynamic equations for inelastic interactions, Journal of Statistical Physics, Vol:98, ISSN:0022-4715, Pages:743-773

Benedetto D, Caglioti E, Carrillo JA, et al., 1998, A non-Maxwellian steady distribution for one-dimensional granular media, Journal of Statistical Physics, Vol:91, ISSN:0022-4715, Pages:979-990

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