EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE Hk

doi:10.1016/S0252-9602(09)60094-1

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1165-1172.doi: 10.1016/S0252-9602(09)60094-1

EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k

张引娣, 李开泰

1.College of Science, Xi'an Jiaotong |University, Xi'an 710049, China
2.College of Science, Chang'an University, Xi'an 710064, China

收稿日期:2007-12-24 修回日期:2008-05-13 出版日期:2009-09-20 发布日期:2009-09-20
基金资助:
Sponsored by the NSFC (10571142, 10771167)

EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k

ZHANG Yin-Di, LI Kai-Tai

1.College of Science, Xi'an Jiaotong |University, Xi'an 710049, China
2.College of Science, Chang'an University, Xi'an 710064, China

Received:2007-12-24 Revised:2008-05-13 Online:2009-09-20 Published:2009-09-20
Supported by:
Sponsored by the NSFC (10571142, 10771167)

摘要/Abstract

摘要：

In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation u_t=Δ_u+λ_u-u³ possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded domain of H^k(Ω) in the H^k-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k∈ [0,1] to the case k∈ [0, ∞).

关键词: semigroup of operator, global attractor, evolution equation, regularity of attractor

Abstract:

Key words: semigroup of operator, global attractor, evolution equation, regularity of attractor

中图分类号:

35B40

张引娣, 李开泰. EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k[J]. 数学物理学报(英文版), 2009, 29(5): 1165-1172.

ZHANG Yin-Di, LI Kai-Tai. EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k[J]. Acta mathematica scientia,Series B, 2009, 29(5): 1165-1172.

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EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k

EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k

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