Necessary and sufficient conditions for the existence of exponential attractors for semigroups, and applications

被引：6

作者：

Li, Yongjun ^{[1
]}

Wu, Hongqing ^{[1
]}

Zhao, Tinggang ^{[1
]}

机构：

[1] Lanzhou City Univ, Sch Math, Lanzhou 730070, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 17期

基金：

中国国家自然科学基金;

关键词：

Dynamical system; Exponential attractors; Measure of non-compactness; omega-limit compactness; NAVIER-STOKES EQUATIONS; GLOBAL ATTRACTORS;

D O I：

10.1016/j.na.2012.07.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

First we establish some necessary and sufficient conditions for the existence of exponential attractors by using omega-limit compactness and a measure of non-compactness. Then we provide a new method for proving the existence of exponential attractors. We prove the existence of exponential attractors for reaction-diffusion equations and 2D Navier-Stokes equations as simple applications. (c) 2012 Elsevier Ltd. All rights reserved.

引用

页码：6297 / 6305

页数：9

共 50 条

[1] Necessary and sufficient conditions for the existence of global attractors for semigroups and applications
Ma, QF
Wang, SH
Zhong, CK
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2002, 51 (06) : 1541 - 1559
[2] NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF EXPONENTIAL DICHOTOMY OF IMPULSIVE EQUATIONS
BAINOV, DD
KOSTADINOV, SI
ZABREIKO, PP
[J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 1992, 31 (08) : 1521 - 1526
[3] Sufficient conditions for the existence of Feller semigroups
Galakhov, EI
[J]. MATHEMATICAL NOTES, 1996, 60 (3-4) : 328 - 330
[4] NECESSARY CONDITIONS AND SUFFICIENT EXISTENCE OF RESOLVENTS
HIRSCH, F
[J]. ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1974, 29 (01): : 73 - 85
[5] The necessary and sufficient conditions for the existence of a centre
Koukless, IS
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES DE L URSS, 1944, 42 : 160 - 163
[6] Are sufficient conditions for conservativity of minimal quantum semigroups necessary?
Fagnola, F.
Pantaleon Martinez, L.
[J]. MATHEMATICAL NOTES, 2012, 91 (5-6) : 851 - 856
[7] Are sufficient conditions for conservativity of minimal quantum semigroups necessary?
F. Fagnola
L. Pantaleoń Martínez
[J]. Mathematical Notes, 2012, 91 : 851 - 856
[8] Sufficient conditions for the existence of global random attractors for stochastic lattice dynamical systems and applications
Zhao, Caidi
Zhou, Shengfan
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 354 (01) : 78 - 95
[9] Necessary and sufficient conditions for existence of decoupling controllers
Lin, CA
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1997, 42 (08) : 1157 - 1161
[10] NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF AN OPTIMAL PORTFOLIO
BERTSEKAS, DP
[J]. JOURNAL OF ECONOMIC THEORY, 1974, 8 (02) : 235 - 247

← 1 2 3 4 5 →