Long-time behavior of stochastic reaction–diffusion equation with multiplicative noise

Advances in Difference Equations

article

Wang, Jing¹  Ma, Qiaozhen¹  Liu, Tingting¹ 

[1] Department of Mathematics, Northwest Normal University

关键词: Stochastic reaction–diffusion equation;    Higher-order integrability;    Pullback random attractor;    Norm-to-norm continuity;   

DOI  :  10.1186/s13662-020-02728-4

学科分类：航空航天科学

来源: SpringerOpen

【 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 $H_{0}^{1}(U)$ is first obtained. As an application, we show the existence of $(L^{2}(U),L^{p}(U))$ and $(L^{2}(U),H_{0}^{1}(U))$-pullback random attractors, respectively.

【 授权许可】

CC BY