TY - JOUR
T1 - Random Attractor for the Nonclassical Diffusion Equation with Fading Memory
AU - Cheng , Shuilin
JO - Journal of Partial Differential Equations
VL - 3
SP - 253
EP - 268
PY - 2015
DA - 2015/09
SN - 28
DO - http://doi.org/10.4208/jpde.v28.n3.4
UR - https://global-sci.org/intro/article_detail/jpde/5113.html
KW - Stochastic nonclassical diffusion equations
KW - fading memory
KW - random attractor
AB -  In this paper,we consider the stochastic nonclassical diffusion equationwith fading memory on a bounded domain. By decomposition of the solution operator, we give the necessary condition of asymptotic smoothness of the solution to the initial boundary value problem, and then we prove the existence of a random attractor in the space $M_1=D(A^{\frac{1}{2}}) × L^2_μ(R^+, D(A^{\frac{1}{2}}))$, where A=-Δ with Dirichlet boundary condition.