Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis

被引：13

作者：

Gurevich, Pavel ^{[1
,2
]}

Tikhomirov, Sergey ^{[1
]}

机构：

[1] Free Univ Berlin, Berlin, Germany

[2] Peoples Friendship Univ Russia, Moscow, Russia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 18期

关键词：

Spatially distributed hysteresis; Reaction-diffusion equation; Uniqueness of solution; LIMIT;

D O I：

10.1016/j.na.2012.08.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and nondiffusive substances interact according to hysteresis law. Under the assumption that the initial data are spatially transverse, we prove a theorem on the uniqueness of solutions. The theorem covers the case of non-Lipschitz hysteresis branches arising in the theory of slow-fast systems. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：6610 / 6619

页数：10

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