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
  • [31] Pullback attractors for a strongly damped delay wave equation in Rn
    Wang, Yejuan
    Qin, Yizhao
    Wang, Jingyu
    STOCHASTICS AND DYNAMICS, 2018, 18 (03)
  • [32] Pullback-Attractors for the Modified Kelvin-Voigt Model
    Ustiuzhaninova, A. S.
    RUSSIAN MATHEMATICS, 2021, 65 (05) : 77 - 82
  • [33] Pullback attractors for 3D MHD equations with damping
    Xiaoya Song
    Zeitschrift für angewandte Mathematik und Physik, 2022, 73
  • [34] Pullback attractors for 3D MHD equations with damping
    Song, Xiaoya
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (02):
  • [35] Pullback attractors in dissipative nonautonomous differential equations under discretization
    Cheban D.N.
    Kloeden P.E.
    Schmalfuß B.
    Journal of Dynamics and Differential Equations, 2001, 13 (1) : 185 - 213
  • [36] PULLBACK ATTRACTORS FOR A CLASS OF NON-NEWTONIAN MICROPOLAR FLUIDS
    De Araujo, Geraldo M.
    Araujo, Marcos A. F.
    Bezerra, Flank D. M.
    Freitas, Mirelson M.
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,
  • [37] PULLBACK ATTRACTORS FOR STOCHASTIC RECURRENT NEURAL NETWORKS WITH DISCRETE AND DISTRIBUTED DELAYS
    Sui, Meiyu
    Wang, Yejuan
    Kloeden, Peter E.
    ELECTRONIC RESEARCH ARCHIVE, 2021, 29 (02): : 2187 - 2221
  • [38] Pullback attractors for a semilinear heat equation on time-varying domains
    Kloeden, Peter E.
    Real, Jose
    Sun, Chunyou
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (12) : 4702 - 4730
  • [39] Pullback exponential attractors for a class of non-Newtonian micropolar fluids
    Ai, Chengfei
    Tan, Zhong
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 503 (02)
  • [40] Pullback attractors for a class of non-autonomous nonclassical diffusion equations
    Cung The Anh
    Tang Quoc Bao
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (02) : 399 - 412
12345