Dynamics and Wong-Zakai Approximations of Stochastic Nonlocal PDEs with Long Time Memory

• Jiaohui Xu ^[1] ; Tomás Caraballo ^[3] ; José Valero ^[2]
  1. [1] Northwest University

     Northwest University

     China

     
  2. [2] Universidad Miguel Hernández de Elche

     Universidad Miguel Hernández de Elche

     Elche, España

     
  3. [3] Wenzhou University & Universidad de Sevilla

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
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• Resumen

  • In this paper, a combination of Galerkin’s method and Dafermos’ transformation is first used to prove the existence and uniqueness of solutions for a class of stochastic nonlocal PDEs with long time memory driven by additive noise. Next, the existence of tempered random attractors for such equations is established in an appropriate space for the analysis of problems with delay and memory. Eventually, the convergence of solutions of Wong-Zakai approximations and upper semicontinuity of random attractors of the approximate random system, as the step sizes of approximations approach zero, are analyzed in a detailed way.