文章基本信息

标题：Long-time behavior of stochastic reaction–diffusion equation with multiplicative noise
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作者：Jing Wang ; Qiaozhen Ma ; Tingting Liu 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-28
DOI：10.1186/s13662-020-02728-4
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the dynamical behavior of the solution for the stochastic reaction–diffusion equation with the nonlinearity satisfying the polynomial growth of arbitrary order $p\geq2$ and any space dimension N. Based on the inductive principle, the higher-order integrability of the difference of the solutions near the initial data is established, and then the (norm-to-norm) continuity of solutions with respect to the initial data in $H_(^)(U)$ is first obtained. As an application, we show the existence of $(L^,(U),L^{p}(U))$ and $(L^,(U),H_(^)(U))$-pullback random attractors, respectively.
关键词：Stochastic reaction–diffusion equation;Higher-order integrability;Pullback random attractor;Norm-to-norm continuity;