Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions

Triple Junction Motion for Allen-Cahn/Cahn-Hilliard Systems

Long time asymptotics are developed here for an Allen-Cahn/Cahn-Hilliard system derived recently by Cahn & Novick-Cohen [11] as a di use interface model for simultaneous orderdisorder and phase separation. Proximity to a deep quench limit is assumed, and spatial scales are chosen to model Krzanowski instabilities in which droplets of a minor disordered phase bounded by interphase boundaries (IP...

The existence of global attractor for a Cahn-Hilliard/Allen-Cahn‎ ‎equation

In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0

Numerical Approximations of Allen-cahn and Cahn-hilliard Equations

Stability analyses and error estimates are carried out for a number of commonly used numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that all the schemes we considered are either unconditionally energy stable, or conditionally energy stable with reasonable stability conditions in the semi-discretized versions. Error estimates for selected schemes with a spectral-Ga...

2 Finite Element Approximation of an Allen - Cahn / Cahn - Hilliard

The Allen-cahn Action Functional in Higher Dimensions

Abstract. The Allen–Cahn action functional is related to the probability of rare events in the stochastically perturbed Allen–Cahn equation. Formal calculations suggest a reduced action functional in the sharp interface limit. We prove in two and three space dimensions the corresponding lower bound. One difficulty is that diffuse interfaces may collapse in the limit. We therefore consider the l...