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

  • Jiaohui Xu [1] ; Tomás Caraballo [3] Árbol académico ; José Valero [2] Árbol académico
    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
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
  • Idioma: inglés
  • DOI: 10.1007/s12346-024-01080-2
  • Enlaces
  • 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.

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