Asymptotic limits of viscous Cahn–Hilliard equation with homogeneous Dirichlet boundary condition

Abstract

In this paper, we are concerned with the asymptotic behavior of solutions for the viscous Cahn–Hilliard equations when parameters involved in the equations tend to zero. Namely, it is shown that solutions of the viscous Cahn–Hilliard equations converge to solutions of the Allen–Cahn equation, the Cahn–Hilliard equation, and the viscous diffusion equation, when suitable parameters tend to zero. Compared with the existing results, a much wider range of chemical potentials can be treated within our setting.