CONVERGENCE OF A PARTICLE METHOD FOR DIFFUSIVE GRADIENT FLOWS IN ONE DIMENSION

被引：11

作者：

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

Patacchini, F. S. ^{[1
]}

Sternberg, P. ^{[2
]}

Wolansky, G. ^{[3
]}

机构：

[1] Imperial Coll London, Dept Math, South Kensington Campus, London SW7 2AZ, England

[2] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[3] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2016年 / 48卷 / 06期

基金：

美国国家科学基金会;

关键词：

particle method; diffusion; gradient flow; discrete gradient flow; Gamma-convergence; GAMMA-CONVERGENCE; SWEEPING PROCESS; EQUATION;

D O I：

10.1137/16M1077210

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretization of the energy via nonoverlapping balls centered at the particles and preserves the gradient flow structure at the particle level. The strategy of the proof is based on an abstract result for the convergence of curves of maximal slope in metric spaces.

引用

页码：3708 / 3741

页数：34

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