Pullback attractors of nonautonomous nonclassical diffusion equations with nonlocal diffusion

Abstract

In this paper, we are concerned with the long-time behavior of solutions to a nonautonomous nonclassical diffusion equation with nonlocal diffusion and nonlinear terms with subcritical growth. Under some suitable assumptions, using the energy method, we prove the existence of minimal pullback attractors for the associated process in two different frameworks. In addition, some relationships between the attractors for the universe of fixed bounded sets and those associated with a universe given by another tempered condition are established.