SHARP ESTIMATES OF THE DIMENSION OF INERTIAL MANIFOLDS FOR NONLINEAR PARABOLIC EQUATIONS

被引：26
作者：
ROMANOV, AV
机构：
来源：
RUSSIAN ACADEMY OF SCIENCES IZVESTIYA MATHEMATICS | 1994年 / 43卷 / 01期
关键词：
D O I：
10.1070/IM1994v043n01ABEH001557
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Sufficient conditions are obtained for the existence of a k-dimensional invariant manifold that attracts as t --> infinity all solutions u(t) of the evolution equation u = - Au + F(u) in a Hilbert space, where A is a linear selfadjoint operator, semibounded from below, with compact resolvent, and F is a uniformly Lipschitz (in suitable norms) nonlinearity; these conditions sharpen previously known conditions and cannot be improved.
引用
收藏
页码：31 / 47
页数：17
相关论文
共 23 条
[1]  
Bogolyubov N.N., 1974, ASYMPTOTIC METHODS T
[2]   POSITIVELY INVARIANT REGIONS FOR SYSTEMS OF NONLINEAR DIFFUSION EQUATIONS [J].
CHUEH, KN ;
CONLEY, CC ;
SMOLLER, JA .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1977, 26 (02) :373-392
[3]  
CONSTANTIN P, 1986, CR ACAD SCI I-MATH, V302, P375
[4]  
Constantin P., 1989, J DYN DIFFER EQU, V1, P45
[5]  
Constantin P, 1989, INTEGRAL MANIFOLDS I, VNew York, P1989
[6]   INERTIAL MANIFOLDS FOR NONLINEAR EVOLUTIONARY EQUATIONS [J].
FOIAS, C ;
SELL, GR ;
TEMAM, R .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1988, 73 (02) :309-353
[7]  
Ladyzhenskaya OA, 1987, USP MAT NAUK, V42, P25
[8]  
LUSKIN M, 1989, RAIRO-MATH MODEL NUM, V23, P445
[9]  
Mallet-Paret J., 1988, J AM MATH SOC, V1, P805, DOI [10.1090/S0894-0347-1988-0943276-7, DOI 10.1090/S0894-0347-1988-0943276-7]
[10]   NEGATIVELY INVARIANT SETS OF COMPACT MAPS AND AN EXTENSION OF A THEOREM OF CARTWRIGHT [J].
MALLETPARET, J .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1976, 22 (02) :331-348
123