Asymptotics for a generalized Cahn-Hilliard equation with forcing terms

Abstract

Motivated by the physical theory of Critical Dynamics the CahnHilliard equation on a bounded space domain is considered and forcing terms of general typo are introduced. For such a roscalod equation the limiting interface problem is studied and the following are derived: (i) asymptotic results indicating that the forcing terms may slow down the equilibrium locally or globally, (ii) the sharp interface limit problem in the multidimensional case demonstrating a local influence in phase transitions of terms that stem from the chemical potential, while free energy independent terms act on the rest of the domain, (iii) a limiting non-homogeneous linear diffusion equation for the one-dimensional problem in the case of deterministic forcing term that follows the white noise scaling.