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On a novel gradient flow structure for the aggregation equation
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Inference for ergodic McKean–Vlasov stochastic differential equations with polynomial interactions
Valentine Genon-Catalot and Catherine Larédo Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 60(4) (2024) https://doi.org/10.1214/23-AIHP1403
Collapse of Inelastic Hard Spheres in Dimension $$d \ge 2$$
Online parameter estimation for the McKean–Vlasov stochastic differential equation
Louis Sharrock, Nikolas Kantas, Panos Parpas and Grigorios A. Pavliotis Stochastic Processes and their Applications 162 481 (2023) https://doi.org/10.1016/j.spa.2023.05.002
Distribution dependent reflecting stochastic differential equations
Uniqueness and Nonuniqueness of Steady States of Aggregation‐Diffusion Equations
Matias G. Delgadino, Xukai Yan and Yao Yao Communications on Pure and Applied Mathematics 75(1) 3 (2022) https://doi.org/10.1002/cpa.21950
Classifying Minimum Energy States for Interacting Particles: Spherical Shells
Cameron Davies, Tongseok Lim and Robert J. McCann SIAM Journal on Applied Mathematics 82(4) 1520 (2022) https://doi.org/10.1137/21M1455309
Non-mean-field Vicsek-type models for collective behavior
Paolo Buttà, Ben Goddard, Thomas M. Hodgson, Michela Ottobre and Kevin J. Painter Mathematical Models and Methods in Applied Sciences 32(14) 2763 (2022) https://doi.org/10.1142/S0218202522500646
Primal Dual Methods for Wasserstein Gradient Flows
An Elo-type rating model for players and teams of variable strength
Bertram Düring, Michael Fischer and Marie-Therese Wolfram Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380(2224) (2022) https://doi.org/10.1098/rsta.2021.0155
Propagation of chaos: A review of models, methods and applications. Ⅱ. Applications
Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials
Kyungkeun Kang, Hwa Kil Kim, Tongseok Lim and Geuntaek Seo Calculus of Variations and Partial Differential Equations 60(1) (2021) https://doi.org/10.1007/s00526-020-01882-7
Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation
Daniel Balagué Guardia, Alethea Barbaro, Jose A. Carrillo and Robert Volkin SIAM Journal on Applied Dynamical Systems 19(4) 2628 (2020) https://doi.org/10.1137/20M1314549
The role of a strong confining potential in a nonlinear Fokker–Planck equation
Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations
Rafael Bailo, José A. Carrillo, Hideki Murakawa and Markus Schmidtchen Mathematical Models and Methods in Applied Sciences 30(13) 2487 (2020) https://doi.org/10.1142/S0218202520500487
A second-order numerical method for the aggregation equations
Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
Matthias Erbar, Max Fathi and André Schlichting Latin American Journal of Probability and Mathematical Statistics 17(1) 445 (2020) https://doi.org/10.30757/ALEA.v17-18
A conservative, free energy dissipating, and positivity preserving finite difference scheme for multi-dimensional nonlocal Fokker–Planck equation
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) https://doi.org/10.1051/m2an/2018028
Sorting Phenomena in a Mathematical Model For Two Mutually Attracting/Repelling Species
Martin Burger, Marco Di Francesco, Simone Fagioli and Angela Stevens SIAM Journal on Mathematical Analysis 50(3) 3210 (2018) https://doi.org/10.1137/17M1125716
Convergence of a linearly transformed particle method for aggregation equations
Convergence to equilibrium in the free Fokker–Planck equation with a double-well potential
Catherine Donati-Martin, Benjamin Groux and Mylène Maïda Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54(4) (2018) https://doi.org/10.1214/17-AIHP856
A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials
Boundary layer analysis from the Keller-Segel system to the aggregation system in one space dimension
Jiahang Che, Li Chen, Simone GÖttlich, Anamika Pandey and Jing Wang Communications on Pure & Applied Analysis 16(3) 1013 (2017) https://doi.org/10.3934/cpaa.2017049
A discontinuous Galerkin method on kinetic flocking models
On minimizers of interaction functionals with competing attractive and repulsive potentials
Razvan C. Fetecau, Ihsan Topaloglu and Rustum Choksi Annales de l'Institut Henri Poincaré C, Analyse non linéaire 32(6) 1283 (2015) https://doi.org/10.1016/j.anihpc.2014.09.004
Numerical Methods for One-Dimensional Aggregation Equations
Contractivity of Transport Distances for the Kinetic Kuramoto Equation
José A. Carrillo, Young-Pil Choi, Seung-Yeal Ha, Moon-Jin Kang and Yongduck Kim Journal of Statistical Physics 156(2) 395 (2014) https://doi.org/10.1007/s10955-014-1005-z
On the non-Markovian Enskog equation for granular gases
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) https://doi.org/10.1016/j.physd.2013.06.011
Stability and clustering of self-similar solutions of aggregation equations
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) (2012) https://doi.org/10.1142/S0218202511400057
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) https://doi.org/10.1137/11081986X
A Partial Integrodifferential Equation in Granular Matter and Its Connection with a Stochastic Model
J.A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent and D. Slepčev Nonlinear Analysis: Theory, Methods & Applications 75(2) 550 (2012) https://doi.org/10.1016/j.na.2011.08.057
Asymptotics of blowup solutions for the aggregation equation