Asymptotic behavior of a Cahn-Hilliard/Allen-Cahn system with temperature

Abstract

The main goal of this paper is to study the asymptotic behavior of a coupled Cahn-Hilliard/Allen-Cahn system with temperature. The work is divided into two parts: In the first part, the heat equation is based on the usual Fourier law. In the second one, it is based on the type III heat conduction law. In both parts, we prove the existence of exponential attractors and, therefore, of finite-dimensional global attractors.