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

作　　者：张引娣 李开泰 

机构地区：[1]College of Science, Xi’an Jiaotong University [2]College of Science, Chang’an University

出　　处：《Acta Mathematica Scientia》2009年第5期1165-1172,共8页数学物理学报（B辑英文版）

基　　金：Sponsored by the NSFC(10571142,10771167)

摘　　要：In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 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, ∞）.In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 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 

分 类 号：O175[理学—数学]