PULLBACK EXPONENTIAL ATTRACTORS FOR EVOLUTION PROCESSES IN BANACH SPACES: PROPERTIES AND APPLICATIONS

被引：28

作者：

Carvalho, Alexandre N. ^{[1
]}

Sonner, Stefanie ^{[2
,3
]}

机构：

[1] Univ Sao Paulo, Inst Ciencias Matemat & Computac, BR-13560970 Sao Carlos, SP, Brazil

[2] BCAM Basque Ctr Appl Math, E-48009 Bilbao, Basque Country, Spain

[3] Helmholtz Zentrum Munchen, Inst Biomath & Biometrie, D-85764 Neuherberg, Germany

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

Exponential attractors; non-autonomous dynamical systems; pullback and forwards attractors; non-autonomous Chafee-Infante equation; non-autonomous damped wave equation;

D O I：

10.3934/cpaa.2014.13.1141

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.

引用

页码：1141 / 1165

页数：25

共 50 条

[1] PULLBACK EXPONENTIAL ATTRACTORS FOR EVOLUTION PROCESSES IN BANACH SPACES: THEORETICAL RESULTS
Carvalho, Alexandre N.
Sonner, Stefanie
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (06) : 3047 - 3071
[2] Exponential attractors in banach spaces
Dung L.
Nicolaenko B.
[J]. Journal of Dynamics and Differential Equations, 2001, 13 (4) : 791 - 806
[3] RANDOM PULLBACK EXPONENTIAL ATTRACTORS: GENERAL EXISTENCE RESULTS FOR RANDOM DYNAMICAL SYSTEMS IN BANACH SPACES
Caraballo, Tomas
Sonner, Stefanie
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (12) : 6383 - 6403
[4] Exponential attractors for semigroups in Banach spaces
Zhong, Yansheng
Zhong, Chengkui
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) : 1799 - 1809
[5] On the continuity of pullback attractors for evolution processes
Carvalho, Alexandre N.
Langa, Jose A.
Robinson, James C.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (5-6) : 1812 - 1824
[6] PULLBACK EXPONENTIAL ATTRACTORS
Langa, Jose A.
Miranville, Alain
Real, Jose
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 26 (04) : 1329 - 1357
[7] Pullback exponential attractors for evolution processes with the difference of 2 solutions lacking smoothing property
Li, Xiaojun
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (10) : 3790 - 3819
[8] PULLBACK ATTRACTORS TO IMPULSIVE EVOLUTION PROCESSES: APPLICATIONS TO DIFFERENTIAL EQUATIONS AND TUBE CONDITIONS
Bortolan, Matheus C.
Manuel Uzal, Jose
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (05) : 2791 - 2826
[9] Pullback exponential attractors with admissible exponential growth in the past
Czaja, Radoslaw
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 104 : 90 - 108
[10] Limitations of pullback attractors for processes
Kloeden, Peter E.
Poetzsche, Christian
Rasmussen, Martin
[J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2012, 18 (04) : 693 - 701

← 1 2 3 4 5 →