Time-dependent global attractor for the nonclassicalreaction-diffusion equations with linear memory

In this article, we consider the long-time behavior of solutions for the nonclassical reaction-diffusionequations with linear memory when the forcing term g(x) ∈ H −1 (Ω) and the nonlinear function satisfies thecritical exponent growth. Within the theory of process on time-dependent spaces, we first investigate the exis-tence of the time-dependent attractor by using the operator decomposition technique and the compactness of thetranslation theorem, and then we obtain the regularity of the time-dependent global attractor.