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

• 论文 • 上一篇    下一篇

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

 张引娣, 李开泰   

  1. 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 Hk

 ZHANG Yin-Di, LI Kai-Tai   

  1. 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:

In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation utuu-u3 possesses a global attractor in Sobolev space Hk for all k≥0, which attracts any bounded domain of Hk(Ω) in the Hk-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:

In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation utuu-u3 possesses a global attractor in Sobolev space Hk for all k≥0, which attracts any bounded domain of Hk(Ω) in the Hk-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, ∞).

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

中图分类号: 

  • 35B40