Long-time random dynamics of stochastic parabolic [formula omitted]-Laplacian equations on [formula omitted

Abstract

In this article, we study the long-time random dynamics of non-autonomous stochastic parabolic p-Laplacian equations driven by a Wiener-type multiplicative noise. By a new asymptotic a priori estimate method, not involving the plus or minus sign of the nonlinearity, the omega-limit compact of solutions in Lp(RN)∩Lq(RN) is proved for any p,q>2 and N≥1, where q is the polynomial growth exponent of the nonlinearity. If 2<p<N, by a boot strap technique, we obtain the higher-order integrability of difference of solutions near the initial time. As an application, we show that the obtained L2-random attractor is attracting in the topology of L2+δ(RN) for any δ>0.