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<p>In this paper, we investigate the existence of pullback attractors for a non-autonomous nonclassical diffusion equation with state-dependent delay. First, the existence and uniqueness of strong solutions are proved via the standard Faedo-Galerkin method. To address the state-dependent delay, we incorporate its compensator into a normal functional, which enables us to obtain both the existence of a pullback absorbing set and the pullback asymptotic compactness of the corresponding evolution process. In particular, new properties of specific composition operators are derived to support the main results. Finally, we establish the existence of pullback attractors.</p>

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Pullback attractors of non-autonomous nonclassical diffusion equations with state-dependent delay

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Qiaozhen Ma,
  • Tongtong Liang,
  • Wenting Liu

摘要

In this paper, we investigate the existence of pullback attractors for a non-autonomous nonclassical diffusion equation with state-dependent delay. First, the existence and uniqueness of strong solutions are proved via the standard Faedo-Galerkin method. To address the state-dependent delay, we incorporate its compensator into a normal functional, which enables us to obtain both the existence of a pullback absorbing set and the pullback asymptotic compactness of the corresponding evolution process. In particular, new properties of specific composition operators are derived to support the main results. Finally, we establish the existence of pullback attractors.