Long-time behavior of nonclassical diffusion equations with memory on time-dependent spaces

Abstract

This paper aims to study the long-time behavior of nonclassical diffusion equation with memory and disturbance parameters on time-dependent space. By using the contractive process method on the family of time-dependent spaces and operator decomposition technique, the existence of pullback attractors is first proved. Then the upper semi-continuity of pullback attractors with respect to perturbation parameter ν in M t is obtained. It’s remarkable that the nonlinearity f satisfies the polynomial growth of arbitrary order.