Hyperbolic Relaxation of the Chemical Potential in the Viscous Cahn–Hilliard Equation

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.