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

共 50 条

[21] Pullback attractors for nonautonomous wave equations with critical exponent
Wang, Yonghai
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (02) : 365 - 376
[22] Pullback-Attractors for the Modified Kelvin–Voigt Model
A. S. Ustiuzhaninova
Russian Mathematics, 2021, 65 : 77 - 82
[23] Continuity of pullback attractors for evolution processes associated with semilinear damped wave equations with time-dependent coefficients
Aragao, Gleiciane S.
Bezerra, Flank D. M.
Figueroa-Lopez, Rodiak N.
Nascimento, Marcelo J. D.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 298 : 30 - 67
[24] UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NONAUTONOMOUS KIRCHHOFF WAVE MODELS
Wang, Yonghai
Zhong, Chengkui
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (07) : 3189 - 3209
[25] Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation
Wang, Yonghai
Hu, Minhui
Qin, Yuming
BOUNDARY VALUE PROBLEMS, 2021, 2021 (01)
[26] NUMERICAL DYNAMICS OF INTEGRODIFFERENCE EQUATIONS: FORWARD DYNAMICS AND PULLBACK ATTRACTORS
Huynh, Huy
Kloeden, Peter E.
Poetzsche, Christian
JOURNAL OF COMPUTATIONAL DYNAMICS, 2023, 10 (02): : 345 - 370
[27] Continuity Properties of Pullback and Pullback Exponential Attractors for Non-autonomous Plate with p-Laplacian
Aouadi, Moncef
APPLIED MATHEMATICS AND OPTIMIZATION, 2024, 89 (01)
[28] Pullback attractors of non-autonomous micropolar fluid flows
Chen, Jianwen
Dong, Bo-Qing
Chen, Zhi-Min
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 336 (02) : 1384 - 1394
[29] Pullback attractors for fractional lattice systems with delays in weighted space
Li, Xintao
Wang, Shengwen
OPEN MATHEMATICS, 2024, 22 (01):
[30] Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation
Yonghai Wang
Minhui Hu
Yuming Qin
Boundary Value Problems, 2021

← 1 2 3 4 5 →