Upper semicontinuity of global attractors for the generalized Cahn-Hilliard equation with inertial term

Abstract

In this paper, we consider the initial boundary value problem for the 2D Cahn-Hilliard equation involving inertial and zero-order source terms. In the case when the zero-order source term is a linear function on a large enough neighborhood of the origin, and the coefficient of the inertial term is sufficiently small, we prove that the global attractors for energy and weak solutions coincide. Then, we establish the upper semicontinuity of these global attractors.