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<p>This paper deals with the convergence rate of the measure attractors of fractional stochastic reaction-diffusion equations on unbounded domains. We first prove the existence and uniqueness of measure attractors. Then we show that the distance from the measure attractor of the original system to the measure attractor of the limiting system is less than a small power of the noise intensity <i>ε</i>, when the measure attractor of limiting system is a singleton set. In the reference [Applied Mathematics Letters 147 (2024) 108842], the estimate of the convergence distance of the attractor with respect to <i>ε</i> is made when both the original systems and the limiting system are singleton sets. However, this paper only requires the limiting system to be a singleton set, thus extending the results of reference [Applied Mathematics Letters 147 (2024) 108842] in a certain form.</p>

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Convergence Rate of Measure Attractors for Stochastic Reaction-diffusion Equations on Unbounded Domains

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Zi-qi Liu,
  • Ding-shi Li

摘要

This paper deals with the convergence rate of the measure attractors of fractional stochastic reaction-diffusion equations on unbounded domains. We first prove the existence and uniqueness of measure attractors. Then we show that the distance from the measure attractor of the original system to the measure attractor of the limiting system is less than a small power of the noise intensity ε, when the measure attractor of limiting system is a singleton set. In the reference [Applied Mathematics Letters 147 (2024) 108842], the estimate of the convergence distance of the attractor with respect to ε is made when both the original systems and the limiting system are singleton sets. However, this paper only requires the limiting system to be a singleton set, thus extending the results of reference [Applied Mathematics Letters 147 (2024) 108842] in a certain form.