REGULAR SOLUTIONS AND GLOBAL ATTRACTORS FOR REACTION-DIFFUSION SYSTEMS WITHOUT UNIQUENES

被引：11

作者：

Kapustyan, Oleksiy V. ^{[1
]}

Kasyanov, Pavlo O. ^{[2
]}

Valero, Jose ^{[3
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, UA-01601 Kiev, Ukraine

[2] Natl Tech Univ Ukraine, Kyiv Polytech Inst, Inst Appl Syst Anal, UA-03056 Kiev, Ukraine

[3] Univ Miguel Hernandez de Elche, Ctr Invest Operat, Elche 03202, Spain

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 05期

关键词：

Reaction-diffusion system; multi-valued dynamical system; global attractor; unstable manifold; Fitz-Hugh-Nagumo system; MULTIVALUED SEMIFLOWS; TRAJECTORY ATTRACTOR; EQUATIONS; BEHAVIOR; DYNAMICS;

D O I：

10.3934/cpaa.2014.13.1891

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the structural properties of global attractors of multi-valued semiflows generated by regular solutions of reaction-diffusion system without uniqueness of the Cauchy problem. Under additional gradient-like condition on the nonlinear term we prove that the global attractor coincides with the unstable manifold of the set of stationary points, and with the stable one when we consider only bounded complete trajectories. As an example we consider a generalized Fitz-Hugh-Nagumo system. We also suggest additional conditions, which provide that the global attractor is a bounded set in (L-infinity(Omega))(N) and compact in (H-0(1)(Omega))(N).

引用

页码：1891 / 1906

页数：16

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