Gradient flows for non-smooth interaction potentials

被引：16

作者：

Carrillo, J. A. ^{[1
]}

Lisini, S. ^{[2
]}

Mainini, E. ^{[3
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ Pavia, Dipartimento Matemat F Casorati, I-27100 Pavia, Italy

[3] Univ Genoa, Dipartimento Ingn Meccan Energet Gestionale & Tra, Sez MAT, I-16129 Genoa, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 100卷

基金：

英国工程与自然科学研究理事会;

关键词：

Wasserstein distance; Gradient flows; Aggregation equations; Measure solution; STATIONARY STATES; KINETIC-MODELS; BLOW-UP; AGGREGATION; EQUATIONS;

D O I：

10.1016/j.na.2014.01.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal with a nonlocal interaction equation describing the evolution of a particle density under the effect of a general symmetric pairwise interaction potential, not necessarily in convolution form. We describe the case of a convex (or lambda-convex) potential, possibly not smooth at several points, generalizing the results of Carrillo et al. (2011). We also identify the cases in which the dynamic is still governed by the continuity equation with well-characterized nonlocal velocity field. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：122 / 147

页数：26

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