Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D
ESAIM: COCV, 21 2 (2015) 414-441
Published online: 2015-03-04
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):
A system of continuity equations with nonlocal interactions of Morse type
Marco Di Francesco and Valeria IorioCommunications on Pure and Applied Analysis (2025)
https://doi.org/10.3934/cpaa.2025041
The Sticky Particle Dynamics of the 1D Pressureless Euler-Alignment System as a Gradient Flow
Sondre Tesdal GaltungApplied Mathematics & Optimization 91 (2) (2025)
https://doi.org/10.1007/s00245-025-10223-z
To blow-up or not to blow-up for a granular kinetic equation
José A. Carrillo, Ruiwen Shu, Li Wang and Wuzhe XuPhysica D: Nonlinear Phenomena 470 134410 (2024)
https://doi.org/10.1016/j.physd.2024.134410
Vanishing viscosity limit for aggregation-diffusion equations
Frédéric Lagoutière, Filippo Santambrogio and Sébastien Tran TienJournal de l’École polytechnique — Mathématiques 11 1123 (2024)
https://doi.org/10.5802/jep.275
Wasserstein steepest descent flows of discrepancies with Riesz kernels
Johannes Hertrich, Manuel Gräf, Robert Beinert and Gabriele SteidlJournal of Mathematical Analysis and Applications 531 (1) 127829 (2024)
https://doi.org/10.1016/j.jmaa.2023.127829
Interpreting systems of continuity equations in spaces of probability measures through PDE duality
José A. Carrillo and David Gómez-CastroRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 118 (3) (2024)
https://doi.org/10.1007/s13398-024-01628-6
Minimizing movement scheme for intrinsic aggregation on compact Riemannian manifolds
Joaquín Sánchez GarcíaDiscrete and Continuous Dynamical Systems (2024)
https://doi.org/10.3934/dcds.2024021
Mean field limit for one dimensional opinion dynamics with Coulomb interaction and time dependent weights
Immanuel Ben-Porat, José A. Carrillo and Sondre T. GaltungNonlinear Analysis 240 113462 (2024)
https://doi.org/10.1016/j.na.2023.113462
217 (2024)
https://doi.org/10.1007/978-3-031-73423-6_6
Second Order Two-Species Systems with Nonlocal Interactions: Existence and Large Damping Limits
Marco Di Francesco, Simone Fagioli and Valeria IorioActa Applicandae Mathematicae 184 (1) (2023)
https://doi.org/10.1007/s10440-023-00564-8
Nonlocal Cross-Interaction Systems on Graphs: Nonquadratic Finslerian Structure and Nonlinear Mobilities
Georg Heinze, Jan-Frederik Pietschmann and Markus SchmidtchenSIAM Journal on Mathematical Analysis 55 (6) 7039 (2023)
https://doi.org/10.1137/22M1470955
An invariance principle for gradient flows in the space of probability measures
José A. Carrillo, Rishabh S. Gvalani and Jeremy S.-H. WuJournal of Differential Equations 345 233 (2023)
https://doi.org/10.1016/j.jde.2022.11.028
14009 431 (2023)
https://doi.org/10.1007/978-3-031-31975-4_33
A measure model for the spread of viral infections with mutations
Xiaoqian Gong and Benedetto PiccoliNetworks and Heterogeneous Media 17 (3) 427 (2022)
https://doi.org/10.3934/nhm.2022015
On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility
Simone Fagioli and Oliver TseNonlinear Analysis 221 112904 (2022)
https://doi.org/10.1016/j.na.2022.112904
Many-particle limit for a system of interaction equations driven by Newtonian potentials
Marco Di Francesco, Antonio Esposito and Markus SchmidtchenCalculus of Variations and Partial Differential Equations 60 (2) (2021)
https://doi.org/10.1007/s00526-021-01960-4
Relaxation Limit of the Aggregation Equation with Pointy Potential
Benoît Fabrèges, Frédéric Lagoutière, Sébastien Tran Tien and Nicolas VaucheletAxioms 10 (2) 108 (2021)
https://doi.org/10.3390/axioms10020108
One dimensional singular Cucker–Smale model: Uniform-in-time mean-field limit and contractivity
Young-Pil Choi and Xiongtao ZhangJournal of Differential Equations 287 428 (2021)
https://doi.org/10.1016/j.jde.2021.04.002
Convergence analysis of upwind type schemes for the aggregation equation with pointy potential
François Delarue, Frédéric Lagoutière and Nicolas VaucheletAnnales Henri Lebesgue 3 217 (2020)
https://doi.org/10.5802/ahl.30
A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION
JOSÉ A. CARRILLO, KATRIN GRUNERT and HELGE HOLDENForum of Mathematics, Sigma 8 (2020)
https://doi.org/10.1017/fms.2020.22
Atomistic Origins of Continuum Dislocation Dynamics
Thomas Hudson, Patrick van Meurs and Mark PeletierMathematical Models and Methods in Applied Sciences (2020)
https://doi.org/10.1142/S0218202520500505
A second-order numerical method for the aggregation equations
José Carrillo, Ulrik Fjordholm and Susanne SolemMathematics of Computation 90 (327) 103 (2020)
https://doi.org/10.1090/mcom/3563
Propagation of Chaos for a Class of First Order Models with Singular Mean Field Interactions
Robert J. Berman and Magnus ÖnnheimSIAM Journal on Mathematical Analysis 51 (1) 159 (2019)
https://doi.org/10.1137/18M1196662
Measure Differential Equations
Benedetto PiccoliArchive for Rational Mechanics and Analysis 233 (3) 1289 (2019)
https://doi.org/10.1007/s00205-019-01379-4
Geodesically convex energies and confinement of solutions for a multi-component system of nonlocal interaction equations
Jonathan ZinslNonlinear Differential Equations and Applications NoDEA 23 (4) (2016)
https://doi.org/10.1007/s00030-016-0399-5
On the pressureless damped Euler–Poisson equations with quadratic confinement: Critical thresholds and large-time behavior
José A. Carrillo, Young-Pil Choi and Ewelina ZatorskaMathematical Models and Methods in Applied Sciences 26 (12) 2311 (2016)
https://doi.org/10.1142/S0218202516500548
Equivalence between duality and gradient flow solutions for one-dimensional aggregation equations
François James and Nicolas VaucheletDiscrete and Continuous Dynamical Systems 36 (3) 1355 (2015)
https://doi.org/10.3934/dcds.2016.36.1355