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Zelik, S. (2004) Asymptotic Regularity of Solutions of a Nonautonomous Damped Wave Equation with a Critical Growth Exponent. Communications on Pure & Applied Analysis, 3, 921-934.
https://doi.org/10.3934/cpaa.2004.3.921

has been cited by the following article:

• TITLE: Long-Time Behavior of Solutions to the Classical Diffusion Equation with a Time-Dependent Memory Kernel

  AUTHORS: Xuan Wang, Xinyu Ma

  KEYWORDS: Classical Reaction-Diffusion Equation, Time-Dependent Memory Kernel, Time-Dependent Global Attractors, Supercritical Nonlinearity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.1, January 15, 2026

  ABSTRACT: This paper investigates a class of classical reaction-diffusion equations with a time-dependent memory kernel, where the nonlinear term satisfies a supercritical growth condition. Under a new theoretical framework, we avoid the use of Sobolev embeddings in the treatment of the supercritical nonlinearity. Since the Sobolev control fails in the supercritical case, we establish the well-posedness of solutions by means of integral-type energy estimates combined with the intrinsic structure of the system. Furthermore, by employing a refined solution decomposition technique, we prove the existence and regularity of a time-dependent global attractor. Our results extend the existing conclusions for reaction–diffusion equations with subcritical or critical nonlinearities.