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<p>A fixed point theorem is firstly used to show the existence and uniqueness of solutions to a stochastic fractional reaction-diffusion equation with memory. Next, under some appropriate assumptions, the stability of solutions to such kind of equations is analyzed by using energy estimates and Dafermos method. We then define a mean random dynamical system via the solutions and prove the existence and uniqueness of weak pullback mean random attractors.</p>

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Dynamics of Stochastic Fractional Heat Equations in Material with Memory

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Jiaohui Xu,
  • Tomás Caraballo,
  • José Valero

摘要

A fixed point theorem is firstly used to show the existence and uniqueness of solutions to a stochastic fractional reaction-diffusion equation with memory. Next, under some appropriate assumptions, the stability of solutions to such kind of equations is analyzed by using energy estimates and Dafermos method. We then define a mean random dynamical system via the solutions and prove the existence and uniqueness of weak pullback mean random attractors.