ATTRACTORS FOR THE NONCLASSICAL DIFFUSION EQUATION WITH TIME-DEPENDENT MEMORY KERNEL AND CRITICAL NONLINEARITY

In this paper, we consider the long-time dynamics of solutions for the nonclassical diffusion equation with time-dependent memory kernel when nonlinear term adheres to critical growth, where the time-dependent memory kernel is used to describe the aging process of viscoelastic conductive medium. Under the new theory framework, we first establish the well-posedness and regularity of the solutions, and then we prove the existence and regularity of the time-dependent global attractors in the time-dependent space $H_0^1(\Omega)\times L_{\mu_t}^2(\mathbb R^+; H_0^1(\Omega))$ by use of the delicate integral estimation method and decomposition technique.