Asymptotic behavior of fractional stochastic heat equations in materials with memory. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Li, Linyan; Shu, Ji; Bai, Qianqian; Li, Hui
• Is Part Of: Applicable analysis. Volume 100:Issue 1(2021)
• Page Start: 145
• Page End: 166
• Publication Date: 2021-01-02
• Subjects: Ming Mei; Random dynamical system -- random attractor -- fractional Laplacian -- integro-differential equation -- additive noise; 37L55 -- 60H15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1597057
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper deals with the asymptotic behavior of solutions for a fractional stochastic integro-differential equation driven by additive noise with α ∈ ( 0, 1 ) . We first apply the Galerkin method to prove the existence and uniqueness of solutions for the equation, then establish the existence and uniqueness of tempered pullback random attractors for the equation in an appropriate Hilbert space, which is different from previous works [Liu L, Caraballo T. Well-posedness and dynamics of a fractional stochastic integro-differential equation. Phys D. 2017;355:45–57].