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Conti, M., Pata, V. and Temam, R. (2013) Attractors for Processes on Time-Dependent Spaces. Applications to Wave Equations. Journal of Differential Equations, 255, 1254-1277.
https://doi.org/10.1016/j.jde.2013.05.013

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.