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
收藏
页码：693 / 701
页数：9
相关论文
共 50 条
  • [1] Forward and pullback attraction on pullback attractors
    Rivero F.
    SeMA Journal, 2010, 51 (1): : 155 - 161
  • [2] ON THE UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR MULTI-VALUED PROCESSES
    Wang, Yejuan
    QUARTERLY OF APPLIED MATHEMATICS, 2013, 71 (02) : 369 - 399
  • [3] Continuity of pullback and uniform attractors
    Hoang, Luan T.
    Olson, Eric J.
    Robinson, James C.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (06) : 4067 - 4093
  • [4] Pullback attractors of nonautonomous dynamical systems
    Wang, Yejuan
    Zhong, Chengkui
    Zhou, Shengfan
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2006, 16 (03) : 587 - 614
  • [5] Pullback Attractors for NonAutonomous Dynamical Systems
    Anguiano, Maria
    Caraballo, Tomas
    Real, Jose
    Valero, Jose
    DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATI ONS, 2013, 47 : 217 - 225
  • [6] CONVERGENCES OF ASYMPTOTICALLY AUTONOMOUS PULLBACK ATTRACTORS TOWARDS SEMIGROUP ATTRACTORS
    Cui, Hongyong
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08): : 3525 - 3535
  • [7] Pullback attractors in nonautonomous difference equations
    Kloeden, PE
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2000, 6 (01) : 33 - 52
  • [8] Pullback attractors for a damped wave equation with delays
    Wang, Yejuan
    STOCHASTICS AND DYNAMICS, 2015, 15 (01)
  • [9] PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION
    Carbone, Vera Lucia
    Dias Nascimento, Marcelo Jose
    Schiabel-Silva, Karina
    da Silva, Ricardo Parreira
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2011,
  • [10] PULLBACK ATTRACTORS FOR A CLASS OF NONLINEAR LATTICES WITH DELAYS
    Wang, Yejuan
    Bai, Kuang
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (04): : 1213 - 1230
12345