Hyperbolic relaxation of the chemical potential in the viscous Cahn-Hilliard equation

Abstract

In this paper, we study a hyperbolic relaxation of the viscous Cahn--Hilliard system with zero Neumann boundary conditions. In fact, we consider a relaxation term involving the second time derivative of the chemical potential in the first equation of the system. We develop a well-posedness, continuous dependence and regularity theory for the initial-boundary value problem. Moreover, we investigate the asymptotic behavior of the system as the relaxation parameter tends to 0 and prove the convergence to the viscous Cahn--Hilliard system.

Key words: Cahn--Hilliard system, hyperbolic relaxation, partial differential equations, initial-boundary value problem, well-posedness, continuous dependence, regularity, asymptotic convergence