Long-time random dynamics of stochastic parabolic p-Laplacian equations on RN. (March 2017)

• Record Type: Journal Article
• Authors: Zhao, Wenqiang
• Is Part Of: Nonlinear analysis. Volume 152(2017)
• Page Start: 196
• Page End: 219
• Publication Date: 2017-03
• Subjects: 37H10 -- 60H15 -- 35B40 -- 35B41; Non-autonomous p-Laplacian equations -- Random attractor -- Higher-order attraction; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.01.004
• Languages: English
• ISSNs: 0362-546X

Abstract

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 .