Year: 2015
Author: Zhi Wang, XianYun Du
Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 1 : pp. 47–73
Abstract
In this paper, we consider the long time behaviors for the partly dissipative stochastic reaction diffusion equations. The existence of a bounded random absorbing set is firstly discussed for the systems and then an estimate on the solution is derived when the time is sufficiently large. Then, we establish the asymptotic compactness of the solution operator by giving uniform a priori estimates on the tails of solutions when time is large enough. In the last, we finish the proof of existence a pullback random attractor in L²(R^n) × L²(R^n). We also prove the upper semicontinuity of random attractors when the intensity of noise approaches zero. The long time behaviors are discussed to explain the corresponding physical phenomenon.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v28.n1.6
Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 1 : pp. 47–73
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Reaction diffusion equation