Acta mathematica scientia, Series B >
EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE Hk
Received date: 2007-12-24
Revised date: 2008-05-13
Online published: 2009-09-20
Supported by
Sponsored by the NSFC (10571142, 10771167)
In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut=Δu+λu-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, ∞).
ZHANG Yin-Di , LI Kai-Tai . EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE Hk[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1165 -1172 . DOI: 10.1016/S0252-9602(09)60094-1
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