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<p>In this paper, we study the forward asymptotic autonomy of attractors for stochastic reaction diffusion equations driven by nonlinear colored noise on unbounded domains. First, we prove the existence, uniqueness and forward compactness of pullback random attractors by the methods of spectral decomposition and the uniform tail-estimates of solutions in order to surmount the difficulties caused by the lack of compact Sobolev embeddings on unbounded domains. Then, we establish the forward asymptotic autonomy of pullback random attractors.</p>

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Forward Asymptotic Autonomy of Attractors for Stochastic Reaction Diffusion Equations Driven by Nonlinear Colored Noise

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Xiaoying Zhu,
  • Xuping Zhang,
  • Donal O’Regan

摘要

In this paper, we study the forward asymptotic autonomy of attractors for stochastic reaction diffusion equations driven by nonlinear colored noise on unbounded domains. First, we prove the existence, uniqueness and forward compactness of pullback random attractors by the methods of spectral decomposition and the uniform tail-estimates of solutions in order to surmount the difficulties caused by the lack of compact Sobolev embeddings on unbounded domains. Then, we establish the forward asymptotic autonomy of pullback random attractors.