Pullback attractor for a non-autonomous modified Swift-Hohenberg equation

被引：28

作者：

Park, Sun Hye ^{[1
]}

Park, Jong Yeoul ^{[2
]}

机构：

[1] Pusan Natl Univ, Ctr Educ Accreditat, Pusan 609735, South Korea

[2] Pusan Natl Univ, Dept Math, Pusan 609735, South Korea

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 67卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

A modified Swift-Hohenberg equation; Pullback attractor; Asymptotic compactness; REACTION-DIFFUSION EQUATIONS; SYSTEMS;

D O I：

10.1016/j.camwa.2013.11.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with a non-autonomous modified Swift Hohenberg equation u(t) + Delta(2)u + 2 Delta u + au + b vertical bar del u vertical bar(2) + u(3) = g(x, t). It is shown that a pullback attractor exists when its external force has exponential growth. Due to the nonlinear terms b vertical bar del u vertical bar(2) and u(3), the estimates are delicate. We overcome this difficulty by imposing the exponential growth condition on the external forcing term g(x, t). (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：542 / 548

页数：7

共 17 条

[1]

[Anonymous], 1988, INFINITE DIMENSIONAL

[2] Pullback attractors for asymptotically compact non-autonomous dynamical systems [J].

Caraballo, T ;

Lukaszewicz, G ;

Real, J .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (03) :484-498

[3]

Chepyzhov V. V., 2002, ATTRACTORS EQUATIONS, V49

[4] Random attractors [J].

Crauel H. ;

Debussche A. ;

Flandoli F. .

Journal of Dynamics and Differential Equations, 1997, 9 (2) :307-341

[5] Propagation of hexagonal patterns near onset [J].

Doelman, A ;

Sandstede, B ;

Scheel, A ;

Schneider, G .

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2003, 14 :85-110

[6] Nonautonomous systems, cocycle attractors and variable time-step discretization [J].

Kloeden, PE ;

Schmalfuss, B .

NUMERICAL ALGORITHMS, 1997, 14 (1-3) :141-152

[7] Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction-diffusion equations [J].

Li, Yongjun ;

Zhong, Chengkui .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (02) :1020-1029

[8] Pullback attractors for a non-autonomous generalized 2D parabolic system in an unbounded domain [J].

Park, Jong Yeoul ;

Park, Sun Hye .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (12) :4046-4057

[9] Pullback attractors for the non-autonomous Benjamin-Bona-Mahony equation in unbounded domains [J].

Park, Jong Yeoul ;

Park, Sun Hye .

SCIENCE CHINA-MATHEMATICS, 2011, 54 (04) :741-752

[10] Some canonical bifurcations in the Swift-Hohenberg equation [J].

Peletier, L. A. ;

Williams, J. F. .

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2007, 6 (01) :208-235

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