Close Search Advanced
Journals
Resources
About Us
Open Access

A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
Preview
Add to basket

Year:    2015

Author:    José A. Carrillo, Alina Chertock, Yanghong Huang

Communications in Computational Physics, Vol. 17 (2015), Iss. 1 : pp. 233–258

Abstract

We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential. The proposed scheme is able to cope with non-smooth stationary states, different time scales including metastability, as well as concentrations and self-similar behavior induced by singular nonlocal kernels. We use the scheme to explore properties of these equations beyond their present theoretical knowledge.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.160214.010814a

Communications in Computational Physics, Vol. 17 (2015), Iss. 1 : pp. 233–258

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:   

Author Details

José A. Carrillo

Alina Chertock

Yanghong Huang

  1. Cardinality estimation of support of the global minimizer for the interaction energy with mildly repulsive potentials

    Kang, Kyungkeun | Kim, Hwa Kil | Seo, Geuntaek

    Physica D: Nonlinear Phenomena, Vol. 399 (2019), Iss. P.51

    https://doi.org/10.1016/j.physd.2019.04.004 [Citations: 3]

  2. Variational Structures Beyond Gradient Flows: a Macroscopic Fluctuation-Theory Perspective

    Patterson, Robert I. A. | Renger, D. R. Michiel | Sharma, Upanshu

    Journal of Statistical Physics, Vol. 191 (2024), Iss. 2

    https://doi.org/10.1007/s10955-024-03233-8 [Citations: 0]

  3. A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials

    Sun, Zheng | Carrillo, José A. | Shu, Chi-Wang

    Journal of Computational Physics, Vol. 352 (2018), Iss. P.76

    https://doi.org/10.1016/j.jcp.2017.09.050 [Citations: 45]

  4. Explicit equilibrium solutions for the aggregation equation with power-law potentials

    A. Carrillo, José | Huang, Yanghong

    Kinetic & Related Models, Vol. 10 (2017), Iss. 1 P.171

    https://doi.org/10.3934/krm.2017007 [Citations: 23]

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

    Bailo, Rafael | Carrillo, José A. | Murakawa, Hideki | Schmidtchen, Markus

    Mathematical Models and Methods in Applied Sciences, Vol. 30 (2020), Iss. 13 P.2487

    https://doi.org/10.1142/S0218202520500487 [Citations: 16]

  6. A finite-volume method for fluctuating dynamical density functional theory

    Russo, Antonio | Perez, Sergio P. | Durán-Olivencia, Miguel A. | Yatsyshin, Peter | Carrillo, José A. | Kalliadasis, Serafim

    Journal of Computational Physics, Vol. 428 (2021), Iss. P.109796

    https://doi.org/10.1016/j.jcp.2020.109796 [Citations: 13]

  7. Phase Transitions in a Kinetic Flocking Model of Cucker--Smale Type

    Barbaro, Alethea B. T. | Can͂izo, José A. | Carrillo, José A. | Degond, Pierre

    Multiscale Modeling & Simulation, Vol. 14 (2016), Iss. 3 P.1063

    https://doi.org/10.1137/15M1043637 [Citations: 47]

  8. One-dimensional aggregation equation after blow up: Existence, uniqueness and numerical simulation

    James, François | Vauchelet, Nicolas

    Networks and Heterogeneous Media, Vol. 11 (2016), Iss. 1 P.163

    https://doi.org/10.3934/nhm.2016.11.163 [Citations: 2]

  9. Mean Field Limits for Interacting Diffusions with Colored Noise: Phase Transitions and Spectral Numerical Methods

    Gomes, S. N. | Pavliotis, G. A. | Vaes, U.

    Multiscale Modeling & Simulation, Vol. 18 (2020), Iss. 3 P.1343

    https://doi.org/10.1137/19M1258116 [Citations: 9]

  10. Entropy Dissipation Semi-Discretization Schemes for Fokker–Planck Equations

    Chow, Shui-Nee | Dieci, Luca | Li, Wuchen | Zhou, Haomin

    Journal of Dynamics and Differential Equations, Vol. 31 (2019), Iss. 2 P.765

    https://doi.org/10.1007/s10884-018-9659-x [Citations: 8]

  11. On the steady-states of a two-species non-local cross-diffusion model

    Rodríguez, Nancy | Hu, Yi

    Journal of Applied Analysis, Vol. 26 (2020), Iss. 1 P.1

    https://doi.org/10.1515/jaa-2020-2003 [Citations: 3]

  12. Relaxation Limit of the Aggregation Equation with Pointy Potential

    Fabrèges, Benoît | Lagoutière, Frédéric | Tran Tien, Sébastien | Vauchelet, Nicolas

    Axioms, Vol. 10 (2021), Iss. 2 P.108

    https://doi.org/10.3390/axioms10020108 [Citations: 2]
  13. Uncertainty Quantification for Hyperbolic and Kinetic Equations

    Uncertainty Quantification for Kinetic Models in Socio–Economic and Life Sciences

    Dimarco, Giacomo | Pareschi, Lorenzo | Zanella, Mattia

    2017

    https://doi.org/10.1007/978-3-319-67110-9_5 [Citations: 13]

  14. A Local Continuum Model of Cell-Cell Adhesion

    Falcó, C. | Baker, R. E. | Carrillo, J. A.

    SIAM Journal on Applied Mathematics, Vol. 84 (2024), Iss. 3 P.S17

    https://doi.org/10.1137/22M1506079 [Citations: 9]

  15. A Lagrangian Scheme for the Solution of Nonlinear Diffusion Equations Using Moving Simplex Meshes

    Carrillo, José A. | Düring, Bertram | Matthes, Daniel | McCormick, David S.

    Journal of Scientific Computing, Vol. 75 (2018), Iss. 3 P.1463

    https://doi.org/10.1007/s10915-017-0594-5 [Citations: 20]

  16. Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller--Segel Equations

    Shen, Jie | Xu, Jie

    SIAM Journal on Numerical Analysis, Vol. 58 (2020), Iss. 3 P.1674

    https://doi.org/10.1137/19M1246705 [Citations: 24]

  17. Biological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn--Hilliard Approximation

    Bernoff, Andrew J. | Topaz, Chad M.

    SIAM Journal on Applied Dynamical Systems, Vol. 15 (2016), Iss. 3 P.1528

    https://doi.org/10.1137/15M1031151 [Citations: 23]

  18. Adaptive hyperbolic-cross-space mapped Jacobi method on unbounded domains with applications to solving multidimensional spatiotemporal integrodifferential equations

    Deng, Yunhong | Shao, Sihong | Mogilner, Alex | Xia, Mingtao

    Journal of Computational Physics, Vol. 520 (2025), Iss. P.113492

    https://doi.org/10.1016/j.jcp.2024.113492 [Citations: 0]

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

    Carrillo, José A. | Holden, Helge | Solem, Susanne

    Journal of Mathematical Biology, Vol. 85 (2022), Iss. 4

    https://doi.org/10.1007/s00285-022-01811-6 [Citations: 4]

  20. A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation

    Lyons, Rainey | Muntean, Adrian | Nika, Grigor

    Comptes Rendus. Mécanique, Vol. 352 (2024), Iss. G1 P.239

    https://doi.org/10.5802/crmeca.265 [Citations: 0]

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

    Falcó, Carles | Cohen, Daniel J. | Carrillo, José A. | Baker, Ruth E.

    Journal of The Royal Society Interface, Vol. 20 (2023), Iss. 204

    https://doi.org/10.1098/rsif.2023.0184 [Citations: 8]

  22. Two Meshfree Numerical Approaches for Solving High-Order Singular Emden–Fowler Type Equations

    Parand, Kourosh | Hemami, Mohammad | Hashemi-Shahraki, Soleiman

    International Journal of Applied and Computational Mathematics, Vol. 3 (2017), Iss. S1 P.521

    https://doi.org/10.1007/s40819-017-0368-7 [Citations: 6]

  23. A positivity-preserving scheme for fluctuating hydrodynamics

    Magaletti, Francesco | Gallo, Mirko | Perez, Sergio P. | Carrillo, José A. | Kalliadasis, Serafim

    Journal of Computational Physics, Vol. 463 (2022), Iss. P.111248

    https://doi.org/10.1016/j.jcp.2022.111248 [Citations: 6]

  24. The Filippov characteristic flow for the aggregation equation with mildly singular potentials

    Carrillo, J.A. | James, F. | Lagoutière, F. | Vauchelet, N.

    Journal of Differential Equations, Vol. 260 (2016), Iss. 1 P.304

    https://doi.org/10.1016/j.jde.2015.08.048 [Citations: 22]

  25. A second-order numerical method for the aggregation equations

    Carrillo, José | Fjordholm, Ulrik | Solem, Susanne

    Mathematics of Computation, Vol. 90 (2020), Iss. 327 P.103

    https://doi.org/10.1090/mcom/3563 [Citations: 2]

  26. An Entropy Satisfying Discontinuous Galerkin Method for Nonlinear Fokker–Planck Equations

    Liu, Hailiang | Wang, Zhongming

    Journal of Scientific Computing, Vol. 68 (2016), Iss. 3 P.1217

    https://doi.org/10.1007/s10915-016-0174-0 [Citations: 18]

  27. Multiple patterns formation for an aggregation/diffusion predator-prey system

    Fagioli, Simone | Jaafra, Yahya

    Networks & Heterogeneous Media, Vol. 16 (2021), Iss. 3 P.377

    https://doi.org/10.3934/nhm.2021010 [Citations: 1]

  28. Pseudospectral methods and iterative solvers for optimization problems from multiscale particle dynamics

    Aduamoah, Mildred | Goddard, Benjamin D. | Pearson, John W. | Roden, Jonna C.

    BIT Numerical Mathematics, Vol. 62 (2022), Iss. 4 P.1703

    https://doi.org/10.1007/s10543-022-00928-w [Citations: 5]

  29. Second-order, positive, and unconditional energy dissipative scheme for modified Poisson–Nernst–Planck equations

    Ding, Jie | Zhou, Shenggao

    Journal of Computational Physics, Vol. 510 (2024), Iss. P.113094

    https://doi.org/10.1016/j.jcp.2024.113094 [Citations: 2]

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

    Carrillo, José A. | Castro, Manuel J. | Kalliadasis, Serafim | Perez, Sergio P.

    SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 2 P.A828

    https://doi.org/10.1137/20M1332645 [Citations: 5]

  31. Regularity of Local Minimizers of the Interaction Energy Via Obstacle Problems

    Carrillo, J. A. | Delgadino, M. G. | Mellet, A.

    Communications in Mathematical Physics, Vol. 343 (2016), Iss. 3 P.747

    https://doi.org/10.1007/s00220-016-2598-7 [Citations: 45]
  32. Non-Local Cell Adhesion Models

    Global Bifurcation

    Buttenschön, Andreas | Hillen, Thomas

    2021

    https://doi.org/10.1007/978-3-030-67111-2_5 [Citations: 0]

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

    Carrillo, José A. | Filbet, Francis | Schmidtchen, Markus

    Numerische Mathematik, Vol. 145 (2020), Iss. 3 P.473

    https://doi.org/10.1007/s00211-020-01121-3 [Citations: 16]

  34. Energy dissipative and positivity preserving schemes for large-convection ion transport with steric and solvation effects

    Ding, Jie | Wang, Zhongming | Zhou, Shenggao

    Journal of Computational Physics, Vol. 488 (2023), Iss. P.112206

    https://doi.org/10.1016/j.jcp.2023.112206 [Citations: 3]

  35. Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system

    Herda, Maxime | Zurek, Antoine

    ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 57 (2023), Iss. 3 P.1589

    https://doi.org/10.1051/m2an/2023032 [Citations: 1]
  36. Active Particles, Volume 2

    Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits

    Carrillo, José A. | Craig, Katy | Yao, Yao

    2019

    https://doi.org/10.1007/978-3-030-20297-2_3 [Citations: 26]

  37. A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation

    Carrillo, Jose A. | Murakawa, Hideki | Sato, Makoto | Togashi, Hideru | Trush, Olena

    Journal of Theoretical Biology, Vol. 474 (2019), Iss. P.14

    https://doi.org/10.1016/j.jtbi.2019.04.023 [Citations: 43]

  38. Impedance Response of Ionic Liquids in Long Slit Pores

    Tomlin, Ruben J. | Roy, Tribeni | Kirk, Toby L. | Marinescu, Monica | Gillespie, Dirk

    Journal of The Electrochemical Society, Vol. 169 (2022), Iss. 12 P.120513

    https://doi.org/10.1149/1945-7111/ac89b5 [Citations: 7]

  39. Swarm Equilibria in Domains with Boundaries

    Fetecau, R. C. | Kovacic, M.

    SIAM Journal on Applied Dynamical Systems, Vol. 16 (2017), Iss. 3 P.1260

    https://doi.org/10.1137/17M1123900 [Citations: 9]

  40. Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions

    Barré, J. | Carrillo, J. A. | Degond, P. | Peurichard, D. | Zatorska, E.

    Journal of Nonlinear Science, Vol. 28 (2018), Iss. 1 P.235

    https://doi.org/10.1007/s00332-017-9408-z [Citations: 12]

  41. Zoology of a Nonlocal Cross-Diffusion Model for Two Species

    Carrillo, José A. | Huang, Yanghong | Schmidtchen, Markus

    SIAM Journal on Applied Mathematics, Vol. 78 (2018), Iss. 2 P.1078

    https://doi.org/10.1137/17M1128782 [Citations: 49]

  42. Well-Balanced Finite-Volume Schemes for Hydrodynamic Equations with General Free Energy

    Carrillo, José A. | Kalliadasis, Serafim | Perez, Sergio P. | Shu, Chi-Wang

    Multiscale Modeling & Simulation, Vol. 18 (2020), Iss. 1 P.502

    https://doi.org/10.1137/18M1230050 [Citations: 10]

  43. Splitting Schemes and Segregation in Reaction Cross-Diffusion Systems

    Carrillo, J. A. | Fagioli, S. | Santambrogio, F. | Schmidtchen, M.

    SIAM Journal on Mathematical Analysis, Vol. 50 (2018), Iss. 5 P.5695

    https://doi.org/10.1137/17M1158379 [Citations: 25]

  44. Positive and free energy satisfying schemes for diffusion with interaction potentials

    Liu, Hailiang | Maimaitiyiming, Wumaier

    Journal of Computational Physics, Vol. 419 (2020), Iss. P.109483

    https://doi.org/10.1016/j.jcp.2020.109483 [Citations: 5]

  45. Synchronising and non-synchronising dynamics for a two-species aggregation model

    Emako-Kazianou, Casimir | Liao, Jie | Vauchelet, Nicolas

    Discrete & Continuous Dynamical Systems - B, Vol. 22 (2017), Iss. 6 P.2121

    https://doi.org/10.3934/dcdsb.2017088 [Citations: 0]

  46. Some free boundary problems involving non-local diffusion and aggregation

    Carrillo, José Antonio | Vázquez, Juan Luis

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373 (2015), Iss. 2050 P.20140275

    https://doi.org/10.1098/rsta.2014.0275 [Citations: 10]

  47. Convergence of Entropic Schemes for Optimal Transport and Gradient Flows

    Carlier, Guillaume | Duval, Vincent | Peyré, Gabriel | Schmitzer, Bernhard

    SIAM Journal on Mathematical Analysis, Vol. 49 (2017), Iss. 2 P.1385

    https://doi.org/10.1137/15M1050264 [Citations: 73]

  48. Flux Globalization Based Well-Balanced Central-Upwind Schemes for Hydrodynamic Equations with General Free Energy

    Chen, Xi | Kurganov, Alexander | Liu, Yongle

    Journal of Scientific Computing, Vol. 95 (2023), Iss. 3

    https://doi.org/10.1007/s10915-023-02221-6 [Citations: 2]

  49. From short-range repulsion to Hele-Shaw problem in a model of tumor growth

    Motsch, Sebastien | Peurichard, Diane

    Journal of Mathematical Biology, Vol. 76 (2018), Iss. 1-2 P.205

    https://doi.org/10.1007/s00285-017-1143-4 [Citations: 11]

  50. Entropy dissipative higher order accurate positivity preserving time-implicit discretizations for nonlinear degenerate parabolic equations

    Yan, Fengna | Van der Vegt, J.J.W. | Xia, Yinhua | Xu, Yan

    Journal of Computational and Applied Mathematics, Vol. 441 (2024), Iss. P.115674

    https://doi.org/10.1016/j.cam.2023.115674 [Citations: 1]

  51. A blob method for diffusion

    Carrillo, José Antonio | Craig, Katy | Patacchini, Francesco S.

    Calculus of Variations and Partial Differential Equations, Vol. 58 (2019), Iss. 2

    https://doi.org/10.1007/s00526-019-1486-3 [Citations: 58]

  52. Kinetic Theory of Particle Interactions Mediated by Dynamical Networks

    Barré, Julien | Degond, Pierre | Zatorska, Ewelina

    Multiscale Modeling & Simulation, Vol. 15 (2017), Iss. 3 P.1294

    https://doi.org/10.1137/16M1085310 [Citations: 18]

  53. Variational convergence of the Scharfetter–Gummel scheme to the aggregation-diffusion equation and vanishing diffusion limit

    Hraivoronska, Anastasiia | Schlichting, André | Tse, Oliver

    Numerische Mathematik, Vol. 156 (2024), Iss. 6 P.2221

    https://doi.org/10.1007/s00211-024-01445-4 [Citations: 0]

  54. Uniqueness of entire ground states for the fractional plasma problem

    Chan, Hardy | González, María Del Mar | Huang, Yanghong | Mainini, Edoardo | Volzone, Bruno

    Calculus of Variations and Partial Differential Equations, Vol. 59 (2020), Iss. 6

    https://doi.org/10.1007/s00526-020-01845-y [Citations: 11]

  55. Multispecies cross-diffusions: From a nonlocal mean-field to a porous medium system without self-diffusion

    Doumic, Marie | Hecht, Sophie | Perthame, Benoît | Peurichard, Diane

    Journal of Differential Equations, Vol. 389 (2024), Iss. P.228

    https://doi.org/10.1016/j.jde.2024.01.017 [Citations: 1]

  56. Collective Search With Finite Perception: Transient Dynamics and Search Efficiency

    Gosztolai, Adam | Carrillo, Jose A. | Barahona, Mauricio

    Frontiers in Physics, Vol. 6 (2019), Iss.

    https://doi.org/10.3389/fphy.2018.00153 [Citations: 7]

  57. Biological modeling with nonlocal advection–diffusion equations

    Painter, Kevin J. | Hillen, Thomas | Potts, Jonathan R.

    Mathematical Models and Methods in Applied Sciences, Vol. 34 (2024), Iss. 01 P.57

    https://doi.org/10.1142/S0218202524400025 [Citations: 5]

  58. A finite volume method for continuum limit equations of nonlocally interacting active chiral particles

    Kruk, Nikita | Carrillo, José A. | Koeppl, Heinz

    Journal of Computational Physics, Vol. 440 (2021), Iss. P.110275

    https://doi.org/10.1016/j.jcp.2021.110275 [Citations: 9]

  59. Structure preserving schemes for the continuum Kuramoto model: Phase transitions

    Carrillo, José A. | Choi, Young-Pil | Pareschi, Lorenzo

    Journal of Computational Physics, Vol. 376 (2019), Iss. P.365

    https://doi.org/10.1016/j.jcp.2018.09.049 [Citations: 11]

  60. Numerical study of a particle method for gradient flows

    Antonio Carrillo, José | Huang, Yanghong | Saverio Patacchini, Francesco | Wolansky, Gershon

    Kinetic & Related Models, Vol. 10 (2017), Iss. 3 P.613

    https://doi.org/10.3934/krm.2017025 [Citations: 21]
  61. Active Particles, Volume 2

    Kinetic Equations and Self-organized Band Formations

    Griette, Quentin | Motsch, Sebastien

    2019

    https://doi.org/10.1007/978-3-030-20297-2_6 [Citations: 2]

  62. Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics

    Carrillo, José A. | Düring, Bertram | Kreusser, Lisa Maria | Schönlieb, Carola-Bibiane

    Discrete & Continuous Dynamical Systems, Vol. 41 (2021), Iss. 8 P.3985

    https://doi.org/10.3934/dcds.2021025 [Citations: 0]

  63. Structure Preserving Schemes for Nonlinear Fokker–Planck Equations and Applications

    Pareschi, Lorenzo | Zanella, Mattia

    Journal of Scientific Computing, Vol. 74 (2018), Iss. 3 P.1575

    https://doi.org/10.1007/s10915-017-0510-z [Citations: 55]

  64. Convergence of a linearly transformed particle method for aggregation equations

    Campos Pinto, Martin | Carrillo, José A. | Charles, Frédérique | Choi, Young-Pil

    Numerische Mathematik, Vol. 139 (2018), Iss. 4 P.743

    https://doi.org/10.1007/s00211-018-0958-2 [Citations: 5]

  65. Fisher information regularization schemes for Wasserstein gradient flows

    Li, Wuchen | Lu, Jianfeng | Wang, Li

    Journal of Computational Physics, Vol. 416 (2020), Iss. P.109449

    https://doi.org/10.1016/j.jcp.2020.109449 [Citations: 23]

  66. Implicit–explicit schemes for nonlinear nonlocal equations with a gradient flow structure in one space dimension

    Bürger, Raimund | Inzunza, Daniel | Mulet, Pep | Villada, Luis Miguel

    Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 3 P.1008

    https://doi.org/10.1002/num.22336 [Citations: 4]

  67. Numerical solution for an aggregation equation with degenerate diffusion

    Cabrales, Roberto Carlos | Gutiérrez-Santacreu, Juan Vicente | Rodríguez-Galván, José Rafael

    Applied Mathematics and Computation, Vol. 377 (2020), Iss. P.125145

    https://doi.org/10.1016/j.amc.2020.125145 [Citations: 0]

  68. A Unified Structure Preserving Scheme for a Multispecies Model with a Gradient Flow Structure and Nonlocal Interactions via Singular Kernels

    Zhang, Yong | Zhao, Yu | Zhou, Zhennan

    SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 3 P.B539

    https://doi.org/10.1137/20M1348911 [Citations: 1]

  69. Anisotropic long-range interaction investigated with cold atoms

    Mancois, Vincent | Barré, Julien | Kwong, Chang Chi | Olivetti, Alain | Viot, Pascal | Wilkowski, David

    Physical Review A, Vol. 102 (2020), Iss. 1

    https://doi.org/10.1103/PhysRevA.102.013311 [Citations: 2]

  70. Existence of Compactly Supported Global Minimisers for the Interaction Energy

    Cañizo, José A. | Carrillo, José A. | Patacchini, Francesco S.

    Archive for Rational Mechanics and Analysis, Vol. 217 (2015), Iss. 3 P.1197

    https://doi.org/10.1007/s00205-015-0852-3 [Citations: 58]

  71. Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach

    Duan, Chenghua | Chen, Wenbin | Liu, Chun | Yue, Xingye | Zhou, Shenggao

    SIAM Journal on Scientific Computing, Vol. 43 (2021), Iss. 1 P.B82

    https://doi.org/10.1137/20M1317931 [Citations: 4]

  72. Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour

    Bürger, Raimund | Inzunza, Daniel | Mulet, Pep | Villada, Luis M.

    Applied Numerical Mathematics, Vol. 144 (2019), Iss. P.234

    https://doi.org/10.1016/j.apnum.2019.04.018 [Citations: 7]

  73. First-order aggregation models with alignment

    Fetecau, Razvan C. | Sun, Weiran | Tan, Changhui

    Physica D: Nonlinear Phenomena, Vol. 325 (2016), Iss. P.146

    https://doi.org/10.1016/j.physd.2016.03.011 [Citations: 12]

  74. Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation

    Aceves-Sanchez, P. | Degond, P. | Keaveny, E. E. | Manhart, A. | Merino-Aceituno, S. | Peurichard, D.

    Bulletin of Mathematical Biology, Vol. 82 (2020), Iss. 10

    https://doi.org/10.1007/s11538-020-00805-z [Citations: 7]

  75. A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling

    Craig, Katy | Elamvazhuthi, Karthik | Haberland, Matt | Turanova, Olga

    Mathematics of Computation, Vol. 92 (2023), Iss. 344 P.2575

    https://doi.org/10.1090/mcom/3841 [Citations: 1]

  76. Mathematical modelling of collagen fibres rearrangement during the tendon healing process

    Carrillo, José Antonio | Parisot, Martin | Szymańska, Zuzanna

    Kinetic & Related Models, Vol. 14 (2021), Iss. 2 P.283

    https://doi.org/10.3934/krm.2021005 [Citations: 1]

  77. Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms

    Carrillo, José A. | Ranetbauer, Helene | Wolfram, Marie-Therese

    Journal of Computational Physics, Vol. 327 (2016), Iss. P.186

    https://doi.org/10.1016/j.jcp.2016.09.040 [Citations: 26]

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

    Carrillo, José A. | Kalliadasis, Serafim | Liang, Fuyue | Perez, Sergio P.

    Royal Society Open Science, Vol. 8 (2021), Iss. 5 P.201294

    https://doi.org/10.1098/rsos.201294 [Citations: 9]

  79. Influence of Exit-Recovery Coefficient on the Leakage and Dynamic Characteristics of Annular Seal

    Zhou, Wenjie | Wu, Guangkuan | Qiu, Ning | Liu, Shengzhu | Lai, Zhounian

    Arabian Journal for Science and Engineering, Vol. 44 (2019), Iss. 2 P.1293

    https://doi.org/10.1007/s13369-018-3495-5 [Citations: 3]

  80. A finite-volume scheme for fractional diffusion on bounded domains

    Bailo, Rafael | Carrillo, José A. | Fronzoni, Stefano | Gómez-Castro, David

    European Journal of Applied Mathematics, Vol. (2024), Iss. P.1

    https://doi.org/10.1017/S0956792524000172 [Citations: 0]

  81. Phase Transitions for Nonlinear Nonlocal Aggregation-Diffusion Equations

    Carrillo, José A. | Gvalani, Rishabh S.

    Communications in Mathematical Physics, Vol. 382 (2021), Iss. 1 P.485

    https://doi.org/10.1007/s00220-021-03977-4 [Citations: 5]

  82. Positivity-preserving and energy-dissipative finite difference schemes for the Fokker–Planck and Keller–Segel equations

    Hu, Jingwei | Zhang, Xiangxiong

    IMA Journal of Numerical Analysis, Vol. 43 (2023), Iss. 3 P.1450

    https://doi.org/10.1093/imanum/drac014 [Citations: 8]
  83. Theory, Numerics and Applications of Hyperbolic Problems II

    Structure Preserving Schemes for Mean-Field Equations of Collective Behavior

    Pareschi, Lorenzo | Zanella, Mattia

    2018

    https://doi.org/10.1007/978-3-319-91548-7_31 [Citations: 3]

  84. Nonlocal Cross-Interaction Systems on Graphs: Nonquadratic Finslerian Structure and Nonlinear Mobilities

    Heinze, Georg | Pietschmann, Jan-Frederik | Schmidtchen, Markus

    SIAM Journal on Mathematical Analysis, Vol. 55 (2023), Iss. 6 P.7039

    https://doi.org/10.1137/22M1470955 [Citations: 0]

  85. Mean Field Limits for Interacting Diffusions in a Two-Scale Potential

    Gomes, S. N. | Pavliotis, G. A.

    Journal of Nonlinear Science, Vol. 28 (2018), Iss. 3 P.905

    https://doi.org/10.1007/s00332-017-9433-y [Citations: 28]

  86. A convergent finite-volume scheme for nonlocal cross-diffusion systems for multi-species populations

    Jüngel, Ansgar | Portisch, Stefan | Zurek, Antoine

    ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 58 (2024), Iss. 2 P.759

    https://doi.org/10.1051/m2an/2024016 [Citations: 1]

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

    BRUNA, M. | BURGER, M. | CARRILLO, J. A.

    European Journal of Applied Mathematics, Vol. 32 (2021), Iss. 4 P.711

    https://doi.org/10.1017/S0956792520000285 [Citations: 5]

  88. Phase Transitions and Bump Solutions of the Keller--Segel Model with Volume Exclusion

    Carrillo, Jose A. | Chen, Xinfu | Wang, Qi | Wang, Zhian | Zhang, Lu

    SIAM Journal on Applied Mathematics, Vol. 80 (2020), Iss. 1 P.232

    https://doi.org/10.1137/19M125827X [Citations: 11]

  89. Convergence analysis of structure‐preserving numerical methods for nonlinear Fokker–Planck equations with nonlocal interactions

    Duan, Chenghua | Chen, Wenbin | Liu, Chun | Wang, Cheng | Zhou, Shenggao

    Mathematical Methods in the Applied Sciences, Vol. 45 (2022), Iss. 7 P.3764

    https://doi.org/10.1002/mma.8015 [Citations: 5]

  90. Residual equilibrium schemes for time dependent partial differential equations

    Pareschi, Lorenzo | Rey, Thomas

    Computers & Fluids, Vol. 156 (2017), Iss. P.329

    https://doi.org/10.1016/j.compfluid.2017.07.013 [Citations: 14]

  91. Entropic Approximation of Wasserstein Gradient Flows

    Peyré, Gabriel

    SIAM Journal on Imaging Sciences, Vol. 8 (2015), Iss. 4 P.2323

    https://doi.org/10.1137/15M1010087 [Citations: 49]

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

    Carrillo, José A. | Wang, Li | Wei, Chaozhen

    SIAM Journal on Numerical Analysis, Vol. 62 (2024), Iss. 1 P.376

    https://doi.org/10.1137/23M1562068 [Citations: 1]

  93. Analysis of an Energy-Dissipating Finite Volume Scheme on Admissible Mesh for the Aggregation-Diffusion Equations

    Zeng, Ping | Zhou, Guanyu

    Journal of Scientific Computing, Vol. 99 (2024), Iss. 2

    https://doi.org/10.1007/s10915-024-02522-4 [Citations: 1]

  94. Hydrodynamic singular regimes in 1 + 1 kinetic models and spectral numerical methods

    Gosse, Laurent | Vauchelet, Nicolas

    Journal of Mathematical Analysis and Applications, Vol. 445 (2017), Iss. 1 P.564

    https://doi.org/10.1016/j.jmaa.2016.07.059 [Citations: 2]

  95. Analysis of Anisotropic Interaction Equations for Fingerprint Simulations

    Kreusser, Lisa Maria

    PAMM, Vol. 18 (2018), Iss. 1

    https://doi.org/10.1002/pamm.201800373 [Citations: 0]

  96. Structure preserving schemes for Fokker–Planck equations with nonconstant diffusion matrices

    Loy, Nadia | Zanella, Mattia

    Mathematics and Computers in Simulation, Vol. 188 (2021), Iss. P.342

    https://doi.org/10.1016/j.matcom.2021.04.018 [Citations: 3]

  97. Unconditionally energy-stable discontinuous Galerkin method for the chemo-repulsion-Navier-Stokes system

    Wang, Meiting | Zou, Guang-an | Wang, Bo | Zhao, Wenju

    Computers & Mathematics with Applications, Vol. 150 (2023), Iss. P.132

    https://doi.org/10.1016/j.camwa.2023.09.012 [Citations: 1]
  98. Innovative Algorithms and Analysis

    Analysis and Simulation of Nonlinear and Nonlocal Transport Equations

    Lagoutière, Frédéric | Vauchelet, Nicolas

    2017

    https://doi.org/10.1007/978-3-319-49262-9_10 [Citations: 3]
  99. Non-Local Cell Adhesion Models

    Introduction

    Buttenschön, Andreas | Hillen, Thomas

    2021

    https://doi.org/10.1007/978-3-030-67111-2_1 [Citations: 0]

  100. Nonlinear aggregation-diffusion equations with Riesz potentials

    Huang, Yanghong | Mainini, Edoardo | Vázquez, Juan Luis | Volzone, Bruno

    Journal of Functional Analysis, Vol. 287 (2024), Iss. 2 P.110465

    https://doi.org/10.1016/j.jfa.2024.110465 [Citations: 0]
  101. Non-Local Cell Adhesion Models

    Discussion and Future Directions

    Buttenschön, Andreas | Hillen, Thomas

    2021

    https://doi.org/10.1007/978-3-030-67111-2_7 [Citations: 0]

  102. A finite-volume scheme for gradient-flow equations with non-homogeneous diffusion

    Mendes, Julien | Russo, Antonio | Perez, Sergio P. | Kalliadasis, Serafim

    Computers & Mathematics with Applications, Vol. 89 (2021), Iss. P.150

    https://doi.org/10.1016/j.camwa.2021.02.004 [Citations: 2]

  103. Tensor-mass Model based real-time simulation of vessel deformation and force feedback for the interventional surgery training system

    Guo, Shuxiang | Cai, Xiaojuan | Gao, Baofeng | Yang, Qiuxia | Zhao, Yan | Xiao, Nan

    2017 IEEE International Conference on Mechatronics and Automation (ICMA), (2017), P.433

    https://doi.org/10.1109/ICMA.2017.8015856 [Citations: 9]

  104. Semi-implicit front capturing schemes for the degenerate nonlinear radiative diffusion equation

    Tang, Min | Zhang, Xiaojiang

    Journal of Computational Physics, Vol. 436 (2021), Iss. P.110290

    https://doi.org/10.1016/j.jcp.2021.110290 [Citations: 5]

  105. Monte Carlo gPC Methods for Diffusive Kinetic Flocking Models with Uncertainties

    Carrillo, José Antonio | Zanella, Mattia

    Vietnam Journal of Mathematics, Vol. 47 (2019), Iss. 4 P.931

    https://doi.org/10.1007/s10013-019-00374-2 [Citations: 17]

  106. Reprint of: Residual equilibrium schemes for time dependent partial differential equations

    Pareschi, Lorenzo | Rey, Thomas

    Computers & Fluids, Vol. 169 (2018), Iss. P.141

    https://doi.org/10.1016/j.compfluid.2018.03.053 [Citations: 0]

  107. Can the Clocks Tick Together Despite the Noise? Stochastic Simulations and Analysis

    Abo, Stéphanie M.C. | Carrillo, José A. | Layton, Anita T.

    SIAM Journal on Applied Dynamical Systems, Vol. 22 (2023), Iss. 2 P.850

    https://doi.org/10.1137/22M147788X [Citations: 0]

  108. An accurate front capturing scheme for tumor growth models with a free boundary limit

    Liu, Jian-Guo | Tang, Min | Wang, Li | Zhou, Zhennan

    Journal of Computational Physics, Vol. 364 (2018), Iss. P.73

    https://doi.org/10.1016/j.jcp.2018.03.013 [Citations: 18]

  109. Primal Dual Methods for Wasserstein Gradient Flows

    Carrillo, José A. | Craig, Katy | Wang, Li | Wei, Chaozhen

    Foundations of Computational Mathematics, Vol. 22 (2022), Iss. 2 P.389

    https://doi.org/10.1007/s10208-021-09503-1 [Citations: 25]

  110. A Structure Preserving Numerical Scheme for Fokker--Planck Equations of Structured Neural Networks with Learning Rules

    He, Qing | Hu, Jingwei | Zhou, Zhennan

    SIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 4 P.B1045

    https://doi.org/10.1137/21M1445600 [Citations: 0]

  111. The role of a strong confining potential in a nonlinear Fokker–Planck equation

    Alasio, Luca | Bruna, Maria | Carrillo, José Antonio

    Nonlinear Analysis, Vol. 193 (2020), Iss. P.111480

    https://doi.org/10.1016/j.na.2019.03.003 [Citations: 3]

  112. A conservative, free energy dissipating, and positivity preserving finite difference scheme for multi-dimensional nonlocal Fokker–Planck equation

    Qian, Yiran | Wang, Zhongming | Zhou, Shenggao

    Journal of Computational Physics, Vol. 386 (2019), Iss. P.22

    https://doi.org/10.1016/j.jcp.2019.02.028 [Citations: 9]

  113. Convergence analysis of upwind type schemes for the aggregation equation with pointy potential

    Delarue, François | Lagoutière, Frédéric | Vauchelet, Nicolas

    Annales Henri Lebesgue, Vol. 3 (2020), Iss. P.217

    https://doi.org/10.5802/ahl.30 [Citations: 5]

  114. On a class of nonlocal continuity equations on graphs

    Esposito, Antonio | Patacchini, Francesco Saverio | Schlichting, André

    European Journal of Applied Mathematics, Vol. 35 (2024), Iss. 1 P.109

    https://doi.org/10.1017/S0956792523000128 [Citations: 2]

  115. A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: Numerical analysis and exploration

    Hu, Jingwei | Liu, Jian-Guo | Xie, Yantong | Zhou, Zhennan

    Journal of Computational Physics, Vol. 433 (2021), Iss. P.110195

    https://doi.org/10.1016/j.jcp.2021.110195 [Citations: 9]

  116. Memory effects in fluctuating dynamic density-functional theory: theory and simulations

    Russo, Antonio | Durán-Olivencia, Miguel A | Yatsyshin, Peter | Kalliadasis, Serafim

    Journal of Physics A: Mathematical and Theoretical, Vol. 53 (2020), Iss. 44 P.445007

    https://doi.org/10.1088/1751-8121/ab9e8d [Citations: 6]

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

    Bailo, Rafael | Carrillo, José A. | Hu, Jingwei

    SIAM Journal on Applied Mathematics, Vol. 83 (2023), Iss. 3 P.1315

    https://doi.org/10.1137/22M1488703 [Citations: 1]

  118. Multilayer perceptron and Chebyshev polynomials-based functional link artificial neural network for solving differential equations

    Panghal, Shagun | Kumar, Manoj

    International Journal of Modeling, Simulation, and Scientific Computing, Vol. 12 (2021), Iss. 02 P.2150011

    https://doi.org/10.1142/S1793962321500112 [Citations: 2]