On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility

被引：9

作者：

Fagioli, Simone ^{[1
]}

Tse, Oliver ^{[2
]}

机构：

[1] Univ Aquila, Dipartimento Ingn & Sci Informaz & Matemat, Via Vetoio 1, I-67100 Coppito, Italy

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2022年 / 221卷

关键词：

Deterministic particle approximation; Entropy solutions; Gradient flow; Nonlocal transport equations; DETERMINISTIC PARTICLE APPROXIMATION; KELLER-SEGEL MODEL; MOVING MESH METHOD; CONSERVATION; EVOLUTION; CONVERGENCE; CHEMOTAXIS; PREVENTION; DYNAMICS; METRICS;

D O I：

10.1016/j.na.2022.112904

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the well-posedness of entropy solutions for a wide class of nonlocaltransport equations with nonlinear mobility in one spatial dimension. The solutionis obtained as the limit of approximations constructed via a deterministic systemof interacting particles that exhibits a gradient flow structure. At the same time,we expose a rigorous gradient flow structure for this class of equations in terms ofan Energy-Dissipation balance, which we obtain via the asymptotic convergenceof functionals.(c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article underthe CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页数：35

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