Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization

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Publications

Computation of Power Law Equilibrium Measures on Balls of Arbitrary Dimension

Author(s): T. S. Gutleb, J. A. Carrillo, S. Olver
Published in: Constructive Approximation, 2022, ISSN 0176-4276
Publisher: Springer Verlag
DOI: 10.1007/s00365-022-09606-0

Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility

Author(s): Carrillo, Jose A.; Gómez-Castro, David; Vázquez, Juan Luis
Published in: Advances in Nonlinear Analysis, 2022, ISSN 2191-9496
Publisher: De Gruyter Open
DOI: 10.1515/anona-2021-0231

Infinite-time concentration in aggregation–diffusion equations with a given potential

Author(s): José A. Carrillo; David Gómez-Castro; Juan Luis Vázquez
Published in: Journal de Mathématiques Pures et Appliquées, 2022, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2021.11.002

Computing equilibrium measures with power law Kernels

Author(s): Gutleb, Timon S.; Carrillo, José A.; Olver, Sheehan
Published in: Mathematics of Computation, 2020, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3740

Dissipative Measure-Valued Solutions to the Euler–Poisson Equation

Author(s): José A. Carrillo, Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
Published in: SIAM Journal on Mathematical Analysis, Issue 56, 2024, Page(s) 304-335, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1525983

A second-order numerical method for the aggregation equations

Author(s): J. A. Carrillo, U. S. Fjordholm, S. Solem
Published in: Mathematics of Computation, 2021, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3563

A λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles

Author(s): José A. Carrillo; Matias G. Delgadino; Grigorios A. Pavliotis
Published in: Journal of Functional Analysis, 2020, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2020.108734

Noise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields

Author(s): J. A. Carrillo, P. Roux, S. Solem
Published in: Physica D: Nonlinear Phenomena, 2023, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2023.133736

Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system

Author(s): José Carrillo Antonio; Ke Lin
Published in: Advances in Nonlinear Analysis, 2022, ISSN 2191-9496
Publisher: De Gruyter Open
DOI: 10.1515/anona-2020-0189

Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics

Author(s): J. A. Carrillo, B. Düring, L. M, Kreusser, C.-B. Schönlieb
Published in: Discrete and Continuous Dynamical Systems- Series A (DCDS-A), 2021, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2021025

On evolution PDEs on co-evolving graphs

Author(s): Antonio Esposito, László Mikolás
Published in: Discrete and Continuous Dynamical Systems, Issue 44, 2024, Page(s) 2660-2683, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2024041

Uncertainty Quantification for the Homogeneous Landau–Fokker–Planck Equation via Deterministic Particle Galerkin Methods

Author(s): Rafael Bailo, José A. Carrillo, Andrea Medaglia, Mattia Zanella
Published in: Multiscale Modeling & Simulation, Issue 23, 2025, Page(s) 687-710, ISSN 1540-3459
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1623653

Enhancement of damaged-image prediction through Cahn-Hilliard image inpainting.

Author(s): José A. Carrillo; Serafim Kalliadasis; Fuyue Liang; Sergio P. Perez
Published in: Royal Society Open Science, 2021, ISSN 2054-5703
Publisher: The Royal Society
DOI: 10.1098/rsos.201294

Nonlinear partial differential equations in neuroscience: From modeling to mathematical theory

Author(s): José A. Carrillo, Pierre Roux
Published in: Mathematical Models and Methods in Applied Sciences, Issue 35, 2025, Page(s) 403-584, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202525400044

Convergence of a particle method for a regularized spatially homogeneous Landau equation

Author(s): J. A. Carrillo, M. G. Delgadino, J. S. H. Wu
Published in: Mathematical Models and Methods in the Applied Sciences, 2023, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202523500215

A Lipschitz metric for the Camassa--Holm equation

Author(s): J. A. Carrillo, K. Grunert, H. Holden
Published in: Forum of Mathematics, Sigma, 2020, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2020.22

To blow-up or not to blow-up for a granular kinetic equation

Author(s): José A. Carrillo, Ruiwen Shu, Li Wang, Wuzhe Xu
Published in: Physica D: Nonlinear Phenomena, Issue 470, 2024, Page(s) 134410, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2024.134410

From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials

Author(s): J. A. Carrillo, R. Shu
Published in: Calculus of Variations and Partial Differential Equations, 2023, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-022-02368-4

Dynamic fibronectin assembly and remodeling by leader neural crest cells prevents jamming in collective cell migration

Author(s): W. D. Martinson, R. McLennan, J. M. Teddy, M. C. McKinney, L. A. Davidson, R. E. Baker, H. M. Byrne, P. M. Kulesa, P. K. Maini
Published in: eLife, 2023, ISSN 2050-084X
Publisher: eLife Sciences Publications
DOI: 10.7554/elife.83792

Fluid models with phase transition for kinetic equations in swarming

Author(s): M. Bostan, J. A. Carrillo
Published in: Mathematical Models and Methods in Applied Sciences, 2020, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202520400163

Minimizers of 3D anisotropic interaction energies

Author(s): José Antonio Carrillo, Ruiwen Shu
Published in: Advances in Calculus of Variations, Issue 17, 2024, Page(s) 775-803, ISSN 1864-8258
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/acv-2022-0059

Convergence and stability results for the particle system in the Stein gradient descent method

Author(s): José Carrillo, Jakub Skrzeczkowski
Published in: Mathematics of Computation, Issue 94, 2025, Page(s) 1793-1814, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/4000

An invariance principle for gradient flows in the space of probability measures

Author(s): Carrillo, J. A.; Gvalani, R. S.; Wu, J.
Published in: Journal of Differential Equations, 2023, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.48550/arxiv.2010.00424

Structure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport Distances

Author(s): José A. Carrillo, Li Wang, Chaozhen Wei
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, Page(s) 376-399, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1562068

On the rate of convergence of Yosida approximation for the nonlocal Cahn–Hilliard equation

Author(s): Piotr Gwiazda, Jakub Skrzeczkowski, Lara Trussardi
Published in: IMA Journal of Numerical Analysis, Issue 45, 2025, Page(s) 68-86, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drae006

Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement

Author(s): J. A. Carrillo, R. Shu
Published in: Archive for Rational Mechanics and Analysis, 2023, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-023-01905-5

Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation

Author(s): R. Bailo, J. A. Carrillo, J. Hu
Published in: SIAM Journal of Applied Mathematics, 2022, ISSN 0036-1399
Publisher: Society for Industrial and Applied Mathematics

Coarse graining of a Fokker–Planck equation with excluded volume effects preserving the gradient flow structure

Author(s): M. Bruna, M. Burger, J. A. Carrillo
Published in: European Journal of Applied Mathematics, 2021, ISSN 0956-7925
Publisher: Cambridge University Press
DOI: 10.1017/s0956792520000285

Convergence of a finite volume scheme for a system of interacting species with cross-diffusion

Author(s): J. A. Carrillo, F. Filbet, M. Schmidtchen
Published in: Numerische Mathematik, 2020, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-020-01121-3

Singular boundary behaviour and large solutions for fractional elliptic equations

Author(s): Abatangelo, Nicola; Gómez-Castro, David; Vázquez, Juan Luis
Published in: Journal of the London Mathematical Society, 2022, ISSN 1469-7750
Publisher: LMS
DOI: 10.1112/jlms.12692

Mathematical modelling of collagen fibres rearrangement during the tendon healing process

Author(s): J. A. Carrillo, M. Parisot, Z. Szymańska
Published in: Kinetic and Related Models, 2021, ISSN 1937-5093
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/krm.2021005

A local continuum model of cell-cell adhesion

Author(s): C. Falcó, R. E. Baker, J. A. Carrillo
Published in: SIAM Journal of Applied Mathematics, 2022, ISSN 0036-1399
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1506079

Well-posedness of an integro-differential model for active Brownian particles

Author(s): Maria Bruna; Martin Burger; Antonio Esposito; Simon Schulz
Published in: SIAM Journal of Mathematical Analysis, 2022, ISSN 1095-7154
Publisher: SIAM
DOI: 10.17863/cam.90770

Global Minimizers of a Large Class of Anisotropic Attractive-Repulsive Interaction Energies in 2D

Author(s): J. A. Carrillo, R. Shu
Published in: Communications on Pure and Applied Mathematics, 2022, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22162

Segregation effects and gap formation in cross-diffusion models

Author(s): M. Burger, J. A. Carrillo, J.-F. Pietschmann, M. Schmidtchen
Published in: Interfaces and Free Boundaries, 2020, ISSN 1463-9963
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/ifb/438

Boltzmann to Landau from the gradient flow perspective

Author(s): J. A. Carrillo, M. Delgadino, J. Wu
Published in: Nonlinear Analysis, 2022, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2022.112824

CBX: Python and Julia Packages for Consensus-BasedInteracting Particle Methods

Author(s): Rafael Bailo, Alethea Barbaro, Susana N. Gomes, Konstantin Riedl, Tim Roith, Claudia Totzeck, Urbain Vaes
Published in: Journal of Open Source Software, Issue 9, 2024, Page(s) 6611, ISSN 2475-9066
Publisher: The Open Journal
DOI: 10.21105/joss.06611

Adaptation to DNA Damage, an Asymptotic Approach for a Cooperative Non-local System

Author(s): Léculier, A; Roux, P
Published in: Acta Applicandae Mathematicae, 2022, ISSN 0167-8019
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10440-022-00501-1

Theoretical study of the emergence of periodic solutions for the inhibitory NNLIF neuron model with synaptic delay

Author(s): K. Ikeda, P. Roux, D. Salort, D. Smets
Published in: Mathematical Neuroscience and Applications, 2022, ISSN 2801-0159
Publisher: EPPSciences
DOI: 10.46298/mna.7256

Graph-to-local limit for the nonlocal interaction equation

Author(s): Antonio Esposito, Georg Heinze, André Schlichting
Published in: Journal de Mathématiques Pures et Appliquées, Issue 194, 2025, Page(s) 103663, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2025.103663

A finite-volume scheme for fractional diffusion on bounded domains

Author(s): Rafael Bailo, José A. Carrillo, Stefano Fronzoni, David Gómez-Castro
Published in: European Journal of Applied Mathematics, Issue 36, 2025, Page(s) 398-418, ISSN 0956-7925
Publisher: Cambridge University Press
DOI: 10.1017/s0956792524000172

Primal Dual Methods for Wasserstein Gradient Flows

Author(s): J. A. Carrillo, K. Craig, L. Wang, C. Wei
Published in: Foundations of Computational Mathematics, 2022, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-021-09503-1

Pressureless Euler with nonlocal interactions as a singular limit of degenerate Navier-Stokes system

Author(s): José A. Carrillo; Aneta Wróblewska-Kamińska; Ewelina Zatorska
Published in: Journal of Mathematical Analysis and Applications, 2020, ISSN 0022-247X
Publisher: Academic Press
DOI: 10.1016/j.jmaa.2020.124400

A particle method for the homogeneous Landau equation

Author(s): José A. Carrillo; Jingwei Hu; Li Wang; J. P. Wu
Published in: Journal of Computational Physics, 2020, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcpx.2020.100066

Can the clocks tick together despite the noise? Stochastic simulations and analysis

Author(s): S. Abo, J. A. Carrillo, A. T. Layton
Published in: SIAM Journal of Applied Dynamical Systems, 2022, ISSN 1536-0040
Publisher: Society of Industrial and Applied Mathematics

FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization

Author(s): J . A. Carrillo, N. Garcia-Trillos, S. Li, Y. Zhu
Published in: Journal of Machine Learning Research, Issue 25, 2024, Page(s) 1−51, ISSN 1532-4435
Publisher: MIT Press
DOI: 10.48550/arXiv.2305.02894

Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations

Author(s): Rafael Bailo; José A. Carrillo; Hideki Murakawa; Markus Schmidtchen
Published in: Mathematical Models and Methods in Applied Sciences, 2020, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202520500487

Large friction-high force fields limit for the nonlinear Vlasov--Poisson--Fokker--Planck system

Author(s): Carrillo, José A.; Choi, Young-Pil; Peng, Yingping
Published in: Kinetic and Related Models, 2022, ISSN 1937-5093
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/krm.2021052

Projective and telescopic projective integration for non-linear kinetic mixtures

Author(s): R. Bailo, T. Rey
Published in: Journal of Computational Physics, 2022, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2022.111082

Convergence of Boundary Layers of Chemotaxis Models with Physical Boundary Conditions I: Degenerate Initial Data

Author(s): José A. Carrillo, Guangyi Hong, Zhi-an Wang
Published in: SIAM Journal on Mathematical Analysis, Issue 56, 2024, Page(s) 7576-7643, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/24m1628426

A consensus-based global optimization method for high dimensional machine learning problems

Author(s): J. A. Carrillo, S. Jin, L. Li, Y. Zhu
Published in: ESAIM: Control, Optimisation and Calculus of Variations, 2021, ISSN 1292-8119
Publisher: EDP Sciences
DOI: 10.1051/cocv/2020046

High-Order Well-Balanced Finite-Volume Schemes for Hydrodynamic Equations With Nonlocal Free Energy

Author(s): José A. Carrillo; Manuel J. Castro; Serafim Kalliadasis; Sergio P. Perez
Published in: SIAM Journal on Scientific Computing, 2021, ISSN 1064-8275
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1332645

The graph limit for a pairwise competition model

Author(s): Immanuel Ben-Porat, José A. Carrillo, Pierre-Emmanuel Jabin
Published in: Journal of Differential Equations, Issue 413, 2024, Page(s) 329-369, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2024.08.069

Quantifying tissue growth, shape and collision via continuum models and Bayesian inference

Author(s): C. Falcó, D. J. Cohen, J. A. Carrillo, R. E. Baker
Published in: Journal of the Royal Society Interface, 2023, ISSN 1742-5689
Publisher: The Royal Society
DOI: 10.1098/rsif.2023.0184

A Simplified Voltage-Conductance Kinetic Model for Interacting Neurons and Its Asymptotic Limit

Author(s): José A. Carrillo, Xu’an Dou, Zhennan Zhou
Published in: SIAM Journal on Mathematical Analysis, Issue 56, 2024, Page(s) 676-726, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/22m1482913

Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas

Author(s): Félix del Teso; David Gómez-Castro; Juan Luis Vázquez
Published in: Fractional Calculus and Applied Analysis, 2021, ISSN 1311-0454
Publisher: Springer Science + Business Media
DOI: 10.1515/fca-2021-0042

A fast regularisation of a Newtonian vortex equation

Author(s): J. A. Carrillo, David Gómez-Castro, J. L. Vázquez
Published in: Annales de l'Institut Henri Poincaré C, 2021, ISSN 0294-1449
Publisher: Elsevier BV
DOI: 10.4171/aihpc/17

Phase Transitions for Nonlinear Nonlocal Aggregation-Diffusion Equations.

Author(s): José A. Carrillo; Rishabh S. Gvalani
Published in: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-03977-4

Phase Separation in Systems of Interacting Active Brownian Particles

Author(s): Maria Bruna; Martin Burger; Antonio Esposito; Simon M. Schulz
Published in: SIAM Journal of Applied Mathematics, 2022, ISSN 0036-1399
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1452524

A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles

Author(s): Nikita Kruk; José A. Carrillo; Heinz Koeppl
Published in: Journal of Computational Physics, 2021, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2021.110275

Traveling bands, clouds, and vortices of chiral active matter.

Author(s): Nikita Kruk; José A. Carrillo; Heinz Koeppl
Published in: Physical Review E, 2020, ISSN 2470-0045
Publisher: American Physical Society
DOI: 10.1103/physreve.102.022604

Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation

Author(s): Rafael Bailo Rafael Bailo, José A. Carrillo José A. Carrillo, Serafim Kalliadasis Serafim Kalliadasis, Sergio P. Perez Sergio P. Perez
Published in: Communications in Computational Physics, Issue 34, 2024, Page(s) 713-748, ISSN 1815-2406
Publisher: Global Science Press
DOI: 10.4208/cicp.oa-2023-0049

A new paradigm considering multicellular adhesion, repulsion and attraction represent diverse cellular tile patterns

Author(s): José A. Carrillo, Hideki Murakawa, Makoto Sato, Miaoxing Wang
Published in: PLOS Computational Biology, Issue 21, 2025, Page(s) e1011909, ISSN 1553-7358
Publisher: Public Library of Science (PLoS)
DOI: 10.1371/journal.pcbi.1011909

Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces

Author(s): José A. Carrillo; Young-Pil Choi; Jinwook Jung
Published in: Mathematical Models and Methods in Applied Sciences, 2021, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202521500081

Mean-Field Limits: From Particle Descriptions to Macroscopic Equations.

Author(s): José A. Carrillo; Young-Pil Choi
Published in: Archive for Rational Mechanics and Analysis, 2021, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-021-01676-x

The Landau equation as a gradient Flow

Author(s): José A. Carrillo, Matias G. Delgadino, Laurent Desvillettes, Jeremy S.-H. Wu
Published in: Analysis & PDE, Issue 17, 2024, Page(s) 1331-1375, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2024.17.1331

A Particle Method for the Multispecies Landau Equation

Author(s): José A. Carrillo, Jingwei Hu, Samuel Q. Van Fleet
Published in: Acta Applicandae Mathematicae, Issue 194, 2024, ISSN 0167-8019
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10440-024-00692-9

Noise-driven bifurcations in a neural field system modelling networks of grid cells

Author(s): José A. Carrillo; Helge Holden; Susanne Solem
Published in: Journal of Mathematical Biology, 2022, ISSN 0303-6812
Publisher: Springer Verlag
DOI: 10.1007/s00285-022-01811-6

Evolution of a structured cell population endowed with plasticity of traits under constraints on and between the traits

Author(s): F. Alvarez, J. A. Carrillo, J. Clairambault
Published in: Journal of Mathematical Biology, 2022, ISSN 0303-6812
Publisher: Springer Verlag
DOI: 10.1007/s00285-022-01820-5

Sparse identification of nonlocal interaction kernels in nonlinear gradient flow equations via partial inversion

Author(s): José A. Carrillo, Gissell Estrada-Rodriguez, László Mikolás, Sui Tang
Published in: Mathematical Models and Methods in Applied Sciences, Issue 35, 2025, Page(s) 1073-1131, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202525500137

The Mean-Field Ensemble Kalman Filter: Near-Gaussian Setting

Author(s): J. A. Carrillo, F. Hoffmann, A. M. Stuart, U. Vaes
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, Page(s) 2549-2587, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/24m1628207

Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel

Author(s): Carrillo de la Plata, JA; Gómez-Castro, D; Yao, Y; Zeng, C
Published in: Archive for Rational Mechanics and Analysis, 2023, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.48550/arxiv.2105.13323

Quantifying cell cycle regulation by tissue crowding

Author(s): Carles Falcó, Daniel J. Cohen, José A. Carrillo, Ruth E. Baker
Published in: Biophysical Journal, Issue 124, 2025, Page(s) 923-932, ISSN 0006-3495
Publisher: Biophysical Society
DOI: 10.1016/j.bpj.2024.05.003

Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation

Author(s): Daniel Balagué Guardia; Alethea B. T. Barbaro; José A. Carrillo; Robert Volkin
Published in: SIAM Journal on Applied Dynamical Systems, 2020, ISSN 1536-0040
Publisher: Society of Industrial and Applied Mathematics
DOI: 10.1137/20m1314549

Porous medium equation and cross-diffusion systems as limit of nonlocal interaction

Author(s): M. Burger, A. Esposito
Published in: Nonlinear Analysis: Theory, Methods and Applications, 2023, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2023.113347

Well-posedness and stability of a stochastic neural field in the form of a partial differential equation

Author(s): José A. Carrillo, Pierre Roux, Susanne Solem
Published in: Journal de Mathématiques Pures et Appliquées, Issue 193, 2024, Page(s) 103623, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2024.103623

Nonlocal approximation of nonlinear diffusion equations

Author(s): José Antonio Carrillo, Antonio Esposito, Jeremy Sheung-Him Wu
Published in: Calculus of Variations and Partial Differential Equations, Issue 63, 2024, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-024-02690-z

Random Batch Particle Methods for the Homogeneous Landau Equation

Author(s): J. A. Carrillo, S. Jin, Y. Tang
Published in: Communications in Computational Physics, 2022, ISSN 1815-2406
Publisher: Global Science Press
DOI: 10.4208/cicp.oa-2021-0200

On the Inviscid Limit Connecting Brinkman’s and Darcy’s Models of Tissue Growth with Nonlinear Pressure

Author(s): Charles Elbar, Jakub Skrzeczkowski
Published in: Journal of Mathematical Fluid Mechanics, Issue 27, 2025, ISSN 1422-6928
Publisher: Birkhauser Verlag
DOI: 10.1007/s00021-025-00933-3

Fast Diffusion leads to partial mass concentration in Keller-Segel type stationary solutions

Author(s): Carrillo, José A.; Delgadino, Matias G.; Frank, Rupert L.; Lewin, Mathieu
Published in: Mathematical Models and Methods in Applied Sciences, 2022, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s021820252250018x

Variational Asymptotic Preserving Scheme for the Vlasov--Poisson--Fokker--Planck System

Author(s): José A. Carrillo; Li Wang; Wuzhe Xu; Ming Yan
Published in: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2020, ISSN 1540-3459
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1350431

Interpreting systems of continuity equations in spaces of probability measures through PDE duality

Author(s): José A. Carrillo, David Gómez-Castro
Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Issue 118, 2024, ISSN 1578-7303
Publisher: Real Academia de Ciencias Exactas, Fisicas y Naturales
DOI: 10.1007/s13398-024-01628-6

On a novel gradient flow structure for the aggregation equation

Author(s): A. Esposito, R. S. Gvalani, A. Schlichting, M. Schmidtchen
Published in: Calculus of Variations and Partial Differential Equations, Issue 63, 2025, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-024-02692-x

Competing effects in fourth‐order aggregation–diffusion equations

Author(s): José Antonio Carrillo, Antonio Esposito, Carles Falcó, Alejandro Fernández‐Jiménez
Published in: Proceedings of the London Mathematical Society, Issue 129, 2024, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.12623

Mean-field derivation of Landau-like equations

Author(s): José Antonio Carrillo, Shuchen Guo, Pierre-Emmanuel Jabin
Published in: Applied Mathematics Letters, Issue 158, 2024, Page(s) 109195, ISSN 0893-9659
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.aml.2024.109195

Controlling swarms towards flocks and mills

Author(s): J. A. Carrillo, D. Kalise, F. Rossi, E. Trélat
Published in: SIAM Journal on Control and Optimization, 2021, ISSN 0363-0129
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1404314

The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations

Author(s): Rafael Bailo, José A. Carrillo, Jingwei Hu
Published in: Journal of Plasma Physics, Issue 90, 2024, ISSN 0022-3778
Publisher: Cambridge University Press
DOI: 10.1017/s0022377824001077

Uniqueness of stationary states for singular Keller-Segel type models

Author(s): V. Calvez, J. A. Carrillo, F. Hoffmann
Published in: Nonlinear Analysis: Theory, Methods and Applications, 2021, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2020.112222

Characterisation of homogeneous fractional Sobolev spaces

Author(s): L. Brasco, David Gómez-Castro, J. L. Vázquez
Published in: Calculus of Variations and Partial Differential Equations, 2021, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-021-01934-6

A positivity-preserving scheme for fluctuating hydrodynamics

Author(s): F. Magaletti, M. Gallo, S. P. Perez, J. A. Carrillo, S. Kalliadasis
Published in: Journal of Computational Physics, 2022, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2022.111248

Partial mass concentration for fast-diffusions with non-local aggregation terms

Author(s): José A. Carrillo, Alejandro Fernández-Jiménez, David Gómez-Castro
Published in: Journal of Differential Equations, Issue 409, 2024, Page(s) 700-773, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2024.08.013

Mean field limit for one dimensional opinion dynamics with Coulomb interaction and time dependent weights

Author(s): Immanuel Ben-Porat, José A. Carrillo, Sondre T. Galtung
Published in: Nonlinear Analysis, Issue 240, 2024, Page(s) 113462, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2023.113462

The equilibrium measure for an anisotropic nonlocal energy

Author(s): J. A. Carrillo, J. Mateu, M.G. Mora, L. Rondi, L. Scardia, J. Verdera
Published in: Calculus of Variations and Partial Differential Equations, 2021, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-021-01928-4

Consensus Based Sampling

Author(s): Carrillo, Jose Antonio; Hoffmann, Franca; Stuart, Andrew M; Vaes, Urbain
Published in: Studies in Applied Mathematics, 2022, ISSN 0022-2526
Publisher: Blackwell Publishing Inc.
DOI: 10.1111/sapm.12470

Global existence and decay rates to self-consistent chemotaxis-fluid system

Author(s): J. A. Carrillo, Y. Peng, Z. Xiang
Published in: Discrete and Continuous Dynamical Systems A, 2023, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2023098

The mean field limit of stochastic differential equation systems modelling grid cells

Author(s): J. A. Carrillo, A. Clini, S. Solem
Published in: SIAM Journal of Mathematical Analysis, 2022, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics

Wasserstein stability estimates for covariance-preconditioned Fokker-Planck equations

Author(s): José A. Carrillo; Urbain Vaes
Published in: Nonlinearity, 2021, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/abbe62

An Optimal Mass Transport Method for Random Genetic Drift

Author(s): Carrillo, José A.; Chen, Lin; Wang, Qi
Published in: SIAM Journal on Numerical Analysis, 2020, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1389431

Linking discrete and continuous models of cell birth and migration

Author(s): W. Duncan Martinson, Alexandria Volkening, Markus Schmidtchen, Chandrasekhar Venkataraman, José A. Carrillo
Published in: Royal Society Open Science, Issue 11, 2024, ISSN 2054-5703
Publisher: The Royal Society
DOI: 10.1098/rsos.232002

Singular solutions for fractional parabolic boundary value problems

Author(s): Hardy Chan; David Gómez-Castro; Juan Luis Vázquez
Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022, ISSN 1578-7303
Publisher: Real Academia de Ciencias Exactas, Fisicas y Naturales
DOI: 10.3929/ethz-b-000562743

Degenerate Cahn–Hilliard systems: From nonlocal to local

Author(s): José A. Carrillo, Charles Elbar, Jakub Skrzeczkowski
Published in: Communications in Contemporary Mathematics, 2024, ISSN 0219-1997
Publisher: World Scientific Publishing Co
DOI: 10.1142/s021919972450041x

On a Class of Nonlocal Continuity Equations on Graphs

Author(s): A. Esposito, F. S. Patacchini, A. Schlichting
Published in: European Journal of Applied Mathematics, 2023, ISSN 0956-7925
Publisher: Cambridge University Press
DOI: 10.1017/s0956792523000128

A static memory sparse spectral method for time-fractional PDEs

Author(s): T. S. Gutleb, J. A. Carrillo
Published in: Journal of Computational Physics, 2023, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2023.112522

Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence

Author(s): Lucio Boccardo, Jesus Ildefonso Diaz, David Gomez-Castro
Published in: Electronic Journal of Differential Equations, Issue 2024, 2024, Page(s) 13, ISSN 1072-6691
Publisher: Texas State University - San Marcos
DOI: 10.58997/ejde.2024.13

Graph-to-local limit for a multi-species nonlocal cross-interaction system

Author(s): A. Esposito, G. Heinze, J.-F. Pietschmann, A. Schlichting, , Proceedings in Applied Mathematics & Mechanics, 2023.
Published in: Proceedings in Applied Mathematics & Mechanics, 2023, ISSN 1617-7061
Publisher: Wiley-VCH Verlag
DOI: 10.1002/pamm.202300094

Nonlinear reaction-diffusion processes for nanocomposites-anomalous improved homogenization

Author(s): J. I. Diaz, David Gómez-Castro, T. A. Shaposhnikova
Published in: De Gruyter Series in Nonlinear Analysis and Applications, 2021, ISSN 0941-813X
Publisher: De Gruyter
DOI: 10.1515/9783110648997

Recent development in kinetic theory of granular materials: analysis and numerical methods

Author(s): J. A. Carrillo, J. Hu, Z. Ma, T. Rey
Published in: Trails in Kinetic Theory, SEMA SIMAI Springer Series, 2021
Publisher: Springer

Chapter 4 - Lagrangian schemes for Wasserstein gradient flows

Author(s): J. A. Carrillo, D. Matthes, M.-T. Wolfram
Published in: Handbook of Numerical Analysis, 2021
Publisher: Elsevier
DOI: 10.1016/bs.hna.2020.10.002

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