Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories

被引：11

作者：

Grasselli, Maurizio ^{[1
]}

Prazak, Dalibor

Schimperna, Giulio ^{[2
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 249卷 / 09期

关键词：

Reaction-diffusion system; Unbounded domain; Global attractor; Kolmogorov's epsilon-entropy; LARGE TIME BEHAVIOR; GLOBAL ATTRACTOR; ASYMPTOTIC-BEHAVIOR; EVOLUTION-EQUATIONS; EXISTENCE;

D O I：

10.1016/j.jde.2010.06.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a nonlinear reaction-diffusion equation on the whole space R-d. We prove the well-posedness of the corresponding Cauchy problem in a general functional setting, namely, when the initial datum is uniformly locally bounded in L-2 only. Then we adapt the short trajectory method to establish the existence of the global attractor and, if d <= 3, we find an upper bound of its Kolmogorov's epsilon-entropy. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2287 / 2315

页数：29

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