Limitations of pullback attractors for processes

被引：25

作者：

Kloeden, Peter E. ^{[1
]}

Poetzsche, Christian ^{[2
]}

Rasmussen, Martin ^{[3
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, D-60054 Frankfurt, Germany

[2] Tech Univ Munich, Zentrum Math, D-85748 Garching, Germany

[3] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2012年 / 18卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

pullback attractor; two-parameter semigroup; skew product flow; GENERAL CONTROL-SYSTEMS;

D O I：

10.1080/10236198.2011.578070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Pullback convergence has been investigated in numerous papers as an appropriate attraction concept for nonautonomous problems. However, in this paper, it is illustrated through some simple examples that pullback attractors do not give a complete picture of asymptotic behaviour when the nonautonomous dynamical systems that they generate are formulated as processes. It is then shown how the problem can be resolved using a skew product formulation of the nonautonomous dynamical systems when the state space of the driving system is compact.

引用

页码：693 / 701

页数：9

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