Long-time random dynamics of stochastic parabolic p-Laplacian equations on RN. (March 2017) - Zhao, Wenqiang
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 L p ( R N ) ∩ L q ( R N ) 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 L 2 -random attractor is attracting in the topology of L 2 + δ ( R N ) for any δ > 0 .