Dynamics of a reaction-diffusion equation with a discontinuous nonlinearity

被引：31

作者：

Arrieta, Jose M. ^{[1
]}

Rodriguez-Bernal, Anibal

Valero, Jose

机构：

[1] Univ Complutense Madrid, Dept Matemat Aplicada, E-28040 Madrid, Spain

[2] Univ Miguel Hernandez, Ctr Invest Operat, Alicante 03202, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2006年 / 16卷 / 10期

关键词：

reaction-diffusion equation; setvalued dynamical system; global attractor; upper semicontinuity; stability; heteroclinic connections;

D O I：

10.1142/S0218127406016586

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the nonlinear dynamics of a reaction-diffusion equation where the nonlinearity presents a discontinuity. We prove the upper semicontinuity of solutions and the global attractor with respect to smooth approximations of the nonlinear term. We also give a, complete description of the set of fixed points and study their stability. Finally, we analyze the existence of heteroclinic connections between the fixed points, obtaining information on the fine structure of the global attractor.

引用

页码：2965 / 2984

页数：20

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