TY - JOUR
T1 - Random Attractor for Stochastic Partly Dissipative Systems on Unbounded Domains
AU - Wang , Zhi
AU - Du , XianYun
JO - Journal of Partial Differential Equations
VL - 1
SP - 47
EP - 73
PY - 2015
DA - 2015/03
SN - 28
DO - http://doi.org/10.4208/jpde.v28.n1.6
UR - https://global-sci.org/intro/article_detail/jpde/5102.html
KW - Reaction diffusion equation
KW - random dynamical systems
KW - random attractors
KW - asymptotic compactness
KW - Sobolev compact embedding
AB - 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.