Article ID Journal Published Year Pages File Type
5774592 Journal of Mathematical Analysis and Applications 2017 29 Pages PDF
Abstract
This article is concerned with the random dynamics of solutions of the non-autonomous parabolic p-Laplacian equations on RN driven by an unbounded additive noise, where the nonlinearity has a (p,q)-growth exponents including the general polynomial-type functions. Firstly by using an inductive method, we establish the higher-order integrability of difference of solutions near the initial time for arbitrary space dimension. Secondly based on this very estimate, the asymptotical compactness of solutions in Lp(RN)∩Lq(RN) for any p,q≥2 is proved by a new technique instead of the usual truncation estimate method, and then we obtain the existence of pullback attractor in Lp(RN)∩Lq(RN) for p-Laplacian equations with an unbounded additive noise. Thirdly we prove that the obtained L2-pullback attractor is attracting and translation bounded in Lδ(RN) topology for any δ∈[2,∞) and arbitrary space dimension N,N≥1.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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