Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

This article has been cited by the following article(s):

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

Kyungkeun Kang, Hwa Kil Kim and Geuntaek Seo
Physica D: Nonlinear Phenomena 399 51 (2019)
DOI: 10.1016/j.physd.2019.04.004
See this article

Boltzmann and Fokker-Planck Equations Modelling Opinion Formation in the Presence of Strong Leaders

Bertram Düring, Peter A. Markowich, Jan-Frederik Pietschmann and Marie-Therese Wolfram
SSRN Electronic Journal (2009)
DOI: 10.2139/ssrn.1399345
See this article

PRIMA 2015: Principles and Practice of Multi-Agent Systems

Stefania Monica and Federico Bergenti
Lecture Notes in Computer Science, PRIMA 2015: Principles and Practice of Multi-Agent Systems 9387 483 (2015)
DOI: 10.1007/978-3-319-25524-8_30
See this article

Emergent behaviour in multi-particle systems with non-local interactions

Theodore Kolokolnikov, José A. Carrillo, Andrea Bertozzi, Razvan Fetecau and Mark Lewis
Physica D: Nonlinear Phenomena 260 1 (2013)
DOI: 10.1016/j.physd.2013.06.011
See this article

Confinement for repulsive-attractive kernels

Yao Yao, José A. Carrillo and Daniel Balagué
Discrete and Continuous Dynamical Systems - Series B 19 (5) 1227 (2014)
DOI: 10.3934/dcdsb.2014.19.1227
See this article

Stability and clustering of self-similar solutions of aggregation equations

Hui Sun, David Uminsky and Andrea L. Bertozzi
Journal of Mathematical Physics 53 (11) 115610 (2012)
DOI: 10.1063/1.4745180
See this article

On the one-dimensional Boltzmann equation for granular flows

Dario Benedetto and Mario Pulvirenti
ESAIM: Mathematical Modelling and Numerical Analysis 35 (5) 899 (2001)
DOI: 10.1051/m2an:2001141
See this article

Asymptotics of blowup solutions for the aggregation equation

Andrea Bertozzi and Yanghong Huang
Discrete and Continuous Dynamical Systems - Series B 17 (4) 1309 (2012)
DOI: 10.3934/dcdsb.2012.17.1309
See this article

Boundary layer analysis from the Keller-Segel system to the aggregation system in one space dimension

Jing Wang, Anamika Pandey, Simone Göttlich, Li Chen and Jiahang Che
Communications on Pure and Applied Analysis 16 (3) 1013 (2017)
DOI: 10.3934/cpaa.2017049
See this article

The Regularity of the Boundary of a Multidimensional Aggregation Patch

A. Bertozzi, J. Garnett, T. Laurent and J. Verdera
SIAM Journal on Mathematical Analysis 48 (6) 3789 (2016)
DOI: 10.1137/15M1033125
See this article

Accurate numerical methods for the collisional motion of (heated) granular flows

Francis Filbet, Lorenzo Pareschi and Giuseppe Toscani
Journal of Computational Physics 202 (1) 216 (2005)
DOI: 10.1016/j.jcp.2004.06.023
See this article

Self-Similarity and Power-Like Tails in Nonconservative Kinetic Models

Lorenzo Pareschi and Giuseppe Toscani
Journal of Statistical Physics 124 (2-4) 747 (2006)
DOI: 10.1007/s10955-006-9025-y
See this article

Existence of Ground States of Nonlocal-Interaction Energies

Robert Simione, Dejan Slepčev and Ihsan Topaloglu
Journal of Statistical Physics 159 (4) 972 (2015)
DOI: 10.1007/s10955-015-1215-z
See this article

Stability of ring patterns arising from two-dimensional particle interactions

Theodore Kolokolnikov, Hui Sun, David Uminsky and Andrea L. Bertozzi
Physical Review E 84 (1) 015203 (2011)
DOI: 10.1103/PhysRevE.84.015203
See this article

Handbook of Mathematical Fluid Dynamics

Cédric Villani
Handbook of Mathematical Fluid Dynamics 1 263 (2002)
DOI: 10.1016/S1874-5792(02)80009-X
See this article

Gradient flows for non-smooth interaction potentials

J.A. Carrillo, S. Lisini and E. Mainini
Nonlinear Analysis: Theory, Methods & Applications 100 122 (2014)
DOI: 10.1016/j.na.2014.01.010
See this article

The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels

Andrea L. Bertozzi and Thomas Laurent
Chinese Annals of Mathematics, Series B 30 (5) 463 (2009)
DOI: 10.1007/s11401-009-0191-5
See this article

Nonlocal interactions by repulsive–attractive potentials: Radial ins/stability

D. Balagué, J.A. Carrillo, T. Laurent and G. Raoul
Physica D: Nonlinear Phenomena 260 5 (2013)
DOI: 10.1016/j.physd.2012.10.002
See this article

On the non-Markovian Enskog equation for granular gases

M S Borovchenkova and V I Gerasimenko
Journal of Physics A: Mathematical and Theoretical 47 (3) 035001 (2014)
DOI: 10.1088/1751-8113/47/3/035001
See this article

Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit

Giovanni Naldi, Lorenzo Pareschi and Giuseppe Toscani
ESAIM: Mathematical Modelling and Numerical Analysis 37 (1) 73 (2003)
DOI: 10.1051/m2an:2003019
See this article

Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem

S. Mischler, C. Mouhot and M. Rodriguez Ricard
Journal of Statistical Physics 124 (2-4) 655 (2006)
DOI: 10.1007/s10955-006-9096-9
See this article

Equilibria of biological aggregations with nonlocal repulsive–attractive interactions

R.C. Fetecau and Y. Huang
Physica D: Nonlinear Phenomena 260 49 (2013)
DOI: 10.1016/j.physd.2012.11.004
See this article

Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak–Keller–Segel Model

Adrien Blanchet, Vincent Calvez and José A. Carrillo
SIAM Journal on Numerical Analysis 46 (2) 691 (2008)
DOI: 10.1137/070683337
See this article

Local Existence of Weak Solutions to Kinetic Models of Granular Media

Martial Agueh
Archive for Rational Mechanics and Analysis 221 (2) 917 (2016)
DOI: 10.1007/s00205-016-0975-1
See this article

Singular patterns for an aggregation model with a confining potential

Theodore Kolokolnikov, Yanghong Huang and Mark Pavlovski
Physica D: Nonlinear Phenomena 260 65 (2013)
DOI: 10.1016/j.physd.2012.10.009
See this article

Blow-up in multidimensional aggregation equations with mildly singular interaction kernels

Andrea L Bertozzi, José A Carrillo and Thomas Laurent
Nonlinearity 22 (3) 683 (2009)
DOI: 10.1088/0951-7715/22/3/009
See this article

A kinetic approximation of Hele–Shaw flow

Lorenzo Pareschi, Giovanni Russo and Giuseppe Toscani
Comptes Rendus Mathematique 338 (2) 177 (2004)
DOI: 10.1016/j.crma.2003.11.006
See this article

Swarm dynamics and equilibria for a nonlocal aggregation model

R C Fetecau, Y Huang and T Kolokolnikov
Nonlinearity 24 (10) 2681 (2011)
DOI: 10.1088/0951-7715/24/10/002
See this article

On a Kinetic Model for a Simple Market Economy

Stephane Cordier, Lorenzo Pareschi and Giuseppe Toscani
Journal of Statistical Physics 120 (1-2) 253 (2005)
DOI: 10.1007/s10955-005-5456-0
See this article

A spatially homogeneous Boltzmann equation for elastic, inelastic and coalescing collisions

Nicolas Fournier and Stéphane Mischler
Journal de Mathématiques Pures et Appliquées 84 (9) 1173 (2005)
DOI: 10.1016/j.matpur.2005.04.003
See this article

Remarks on a class of kinetic models of granular media: Asymptotics and entropy bounds

Reinhard Illner, Guillaume Carlier and Martial Agueh
Kinetic and Related Models 8 (2) 201 (2015)
DOI: 10.3934/krm.2015.8.201
See this article

Progress in Fine Particle Plasmas

Viktor Gerasimenko
Progress in Fine Particle Plasmas (2020)
DOI: 10.5772/intechopen.90027
See this article

Confinement in nonlocal interaction equations

J.A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent and D. Slepčev
Nonlinear Analysis: Theory, Methods & Applications 75 (2) 550 (2012)
DOI: 10.1016/j.na.2011.08.057
See this article

Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation

Bertram Düring and Marie-Therese Wolfram
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2182) 20150345 (2015)
DOI: 10.1098/rspa.2015.0345
See this article

Geometry of minimizers for the interaction energy with mildly repulsive potentials

J.A. Carrillo, A. Figalli and F.S. Patacchini
Annales de l'Institut Henri Poincare (C) Non Linear Analysis 34 (5) 1299 (2017)
DOI: 10.1016/j.anihpc.2016.10.004
See this article

AGGREGATION AND SPREADING VIA THE NEWTONIAN POTENTIAL: THE DYNAMICS OF PATCH SOLUTIONS

ANDREA L. BERTOZZI, THOMAS LAURENT and FLAVIEN LÉGER
Mathematical Models and Methods in Applied Sciences 22 (supp01) 1140005 (2012)
DOI: 10.1142/S0218202511400057
See this article

Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations

Jonathan Zinsl
Nonlinear Differential Equations and Applications NoDEA 23 (4) (2016)
DOI: 10.1007/s00030-016-0399-5
See this article

A variational approach to nonlinear and interacting diffusions

Marc Arnaudon and Pierre Del Moral
Stochastic Analysis and Applications 37 (5) 717 (2019)
DOI: 10.1080/07362994.2019.1609985
See this article

Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders

Bertram Düring, Peter Markowich, Jan-Frederik Pietschmann and Marie-Therese Wolfram
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465 (2112) 3687 (2009)
DOI: 10.1098/rspa.2009.0239
See this article

STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS

KLEMENS FELLNER and GAËL RAOUL
Mathematical Models and Methods in Applied Sciences 20 (12) 2267 (2010)
DOI: 10.1142/S0218202510004921
See this article

Characterization of Radially Symmetric Finite Time Blowup in Multidimensional Aggregation Equations

Andrea L. Bertozzi, John B. Garnett and Thomas Laurent
SIAM Journal on Mathematical Analysis 44 (2) 651 (2012)
DOI: 10.1137/11081986X
See this article

Blow Up Analysis for Anomalous Granular Gases

Thomas Rey
SIAM Journal on Mathematical Analysis 44 (3) 1544 (2012)
DOI: 10.1137/110835645
See this article

First‐Order Continuous Models of Opinion Formation

Giacomo Aletti, Giovanni Naldi and Giuseppe Toscani
SIAM Journal on Applied Mathematics 67 (3) 837 (2007)
DOI: 10.1137/060658679
See this article

Lagrangian Numerical Approximations to One‐Dimensional Convolution‐Diffusion Equations

Laurent Gosse and Giuseppe Toscani
SIAM Journal on Scientific Computing 28 (4) 1203 (2006)
DOI: 10.1137/050628015
See this article

Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms

José A. Carrillo, Helene Ranetbauer and Marie-Therese Wolfram
Journal of Computational Physics 327 186 (2016)
DOI: 10.1016/j.jcp.2016.09.040
See this article

Existence of ground states for aggregation-diffusion equations

J. A. Carrillo, M. G. Delgadino and F. S. Patacchini
Analysis and Applications 17 (03) 393 (2019)
DOI: 10.1142/S0219530518500276
See this article

On an isoperimetric problem with power-law potentials and external attraction

Guoqing Zhang and Xiaoqian Geng
Journal of Mathematical Analysis and Applications 482 (1) 123521 (2020)
DOI: 10.1016/j.jmaa.2019.123521
See this article

Zoology of a Nonlocal Cross-Diffusion Model for Two Species

José A. Carrillo, Yanghong Huang and Markus Schmidtchen
SIAM Journal on Applied Mathematics 78 (2) 1078 (2018)
DOI: 10.1137/17M1128782
See this article

Swarm Equilibria in Domains with Boundaries

R. C. Fetecau and M. Kovacic
SIAM Journal on Applied Dynamical Systems 16 (3) 1260 (2017)
DOI: 10.1137/17M1123900
See this article

Global Solution for the Spatially Inhomogeneous Non-cutoff Kac Equation

Tong Yang and Hongjun Yu
SIAM Journal on Mathematical Analysis 50 (4) 4503 (2018)
DOI: 10.1137/17M1135955
See this article

Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure

J.A. Carrillo, Y. Huang, M.C. Santos and J.L. Vázquez
Journal of Differential Equations 258 (3) 736 (2015)
DOI: 10.1016/j.jde.2014.10.003
See this article

Kinetic Approach to Long time Behavior of Linearized Fast Diffusion Equations

María J. Cáceres and Giuseppe Toscani
Journal of Statistical Physics 128 (4) 883 (2007)
DOI: 10.1007/s10955-007-9329-6
See this article

Systems, Control, Modeling and Optimization

E. Ferrari, G. Naldi and G. Toscani
IFIP International Federation for Information Processing, Systems, Control, Modeling and Optimization 202 151 (2006)
DOI: 10.1007/0-387-33882-9_14
See this article

Lp theory for the multidimensional aggregation equation

Andrea L. Bertozzi, Thomas Laurent and Jesús Rosado
Communications on Pure and Applied Mathematics 64 (1) 45 (2011)
DOI: 10.1002/cpa.20334
See this article

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

Yiran Qian, Zhongming Wang and Shenggao Zhou
Journal of Computational Physics 386 22 (2019)
DOI: 10.1016/j.jcp.2019.02.028
See this article

Long-Time Behavior of Nonautonomous Fokker-Planck Equations and Cooling of Granular Gases

B. Lods and G. Toscani
Ukrainian Mathematical Journal 57 (6) 923 (2005)
DOI: 10.1007/s11253-005-0240-5
See this article

Modeling and Computational Methods for Kinetic Equations

Lorenzo Pareschi and Giuseppe Toscani
Modeling and Simulation in Science, Engineering and Technology, Modeling and Computational Methods for Kinetic Equations 259 (2004)
DOI: 10.1007/978-0-8176-8200-2_9
See this article

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

Raimund Bürger, Daniel Inzunza, Pep Mulet and Luis Miguel Villada
Numerical Methods for Partial Differential Equations 35 (3) 1008 (2019)
DOI: 10.1002/num.22336
See this article

First-order aggregation models and zero inertia limits

R.C. Fetecau and W. Sun
Journal of Differential Equations 259 (11) 6774 (2015)
DOI: 10.1016/j.jde.2015.08.018
See this article

Numerical Mathematics and Advanced Applications

L. Pareschi
Numerical Mathematics and Advanced Applications 469 (2003)
DOI: 10.1007/978-88-470-2089-4_44
See this article

Nonlinear Differential Equation Models

Giuseppe Toscani
Nonlinear Differential Equation Models 179 (2004)
DOI: 10.1007/978-3-7091-0609-9_13
See this article

On minimizers of interaction functionals with competing attractive and repulsive potentials

Rustum Choksi, Razvan C. Fetecau and Ihsan Topaloglu
Annales de l'Institut Henri Poincare (C) Non Linear Analysis 32 (6) 1283 (2015)
DOI: 10.1016/j.anihpc.2014.09.004
See this article

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

José A. Carrillo, Alina Chertock and Yanghong Huang
Communications in Computational Physics 17 (1) 233 (2015)
DOI: 10.4208/cicp.160214.010814a
See this article

Handbook of Mathematical Fluid Dynamics

Cédric Villani
Handbook of Mathematical Fluid Dynamics 1 245 (2002)
DOI: 10.1016/S1874-5792(02)80008-8
See this article

Handbook of Mathematical Fluid Dynamics

Cédric Villani
Handbook of Mathematical Fluid Dynamics 1 141 (2002)
DOI: 10.1016/S1874-5792(02)80006-4
See this article

Handbook of Mathematical Fluid Dynamics

Cédric Villani
Handbook of Mathematical Fluid Dynamics 1 189 (2002)
DOI: 10.1016/S1874-5792(02)80007-6
See this article

Handbook of Mathematical Fluid Dynamics

Cédric Villani
Handbook of Mathematical Fluid Dynamics 1 75 (2002)
DOI: 10.1016/S1874-5792(02)80005-2
See this article

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

Raimund Bürger, Daniel Inzunza, Pep Mulet and Luis M. Villada
Applied Numerical Mathematics 144 234 (2019)
DOI: 10.1016/j.apnum.2019.04.018
See this article

Solutions of a non‐local aggregation equation: Universal bounds, concavity changes, and efficient numerical solutions

Klemens Fellner and Barry D. Hughes
Mathematical Methods in the Applied Sciences 43 (8) 5398 (2020)
DOI: 10.1002/mma.6281
See this article

Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation

Li Chen, Simone Göttlich and Stephan Knapp
ESAIM: Mathematical Modelling and Numerical Analysis 52 (2) 567 (2018)
DOI: 10.1051/m2an/2018028
See this article

The Ellipse Law: Kirchhoff Meets Dislocations

J. A. Carrillo, J. Mateu, M. G. Mora, et al.
Communications in Mathematical Physics 373 (2) 507 (2020)
DOI: 10.1007/s00220-019-03368-w
See this article

A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION

JOSÉ A. CARRILLO, KATRIN GRUNERT and HELGE HOLDEN
Forum of Mathematics, Sigma 8 (2020)
DOI: 10.1017/fms.2020.22
See this article