Dynamics for a stochastic degenerate parabolic equation

摘要

In this paper we consider the long-time behavior of a class of stochastic degenerate parabolic equations involving an operator which is X-elliptic with respect to a family of locally Lipschitz continuous vector fields X = {X-1, X-2, ..., X-(m) over tilde}. The nonlinearity satisfies a dissipative condition with polynomial growth of arbitrary order p = 2. The existence of the random attractor in L-2(theta), higher-order integrability and continuity in H are established. (C) 2018 Elsevier Ltd. All rights reserved.