A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts

被引：12

作者：

Carlier, Guillaume ^{[1
]}

Laborde, Maxime

机构：

[1] Univ Paris 09, PSL Res Univ, CNRS, CEREMADE, F-75016 Paris, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 150卷

关键词：

Wasserstein gradient flows; Jordan-Kinderlehrer-Otto scheme; Splitting; Nonlocal drift; Nonlinear diffusions; Helmholtz decomposition; EQUATIONS; SPACES;

D O I：

10.1016/j.na.2016.10.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive and based on the Helmholtz decomposition of the drift and a splitting scheme. The splitting scheme combines transport steps by the divergence-free part of the drift and semi-implicit minimization steps a la Jordan-Kinderlehrer Otto to deal with the potential part. (C) 2016 Published by Elsevier Ltd.

引用

页码：1 / 18

页数：18

共 18 条

[1]

Agueh M, 2005, ADV DIFFERENTIAL EQU, V10, P309

[2]

Ambrosio L., 2005, LECT MATH

[3]

Benamou JD, 2000, NUMER MATH, V84, P375, DOI 10.1007/s002119900117

[4] POLAR FACTORIZATION AND MONOTONE REARRANGEMENT OF VECTOR-VALUED FUNCTIONS [J].