Asymptotics for a generalized Cahn-Hilliard equationwith forcing terms

Abstract

Motivated by the physical theory of Critical Dynamics theCahn-Hilliard equation on a bounded space domain is considered andforcing terms of general type are introduced. For such a rescaledequation the limiting inter-face problem is studied and thefollowing are derived: (i) asymptotic results indicating that theforcing terms may slow down the equilibrium locally or globally,(ii) the sharp interface limit problem in the multidimensionalcase demonstrating a local influence in phase transitions ofterms that stem from the chemical potential, while free energyindependent terms act on the rest of the domain, (iii) a limitingnon-homogeneous linear diffusion equation for the one-dimensionalproblem in the case of deterministic forcing term that followsthe white noise scaling.