Weak solutions for a modified degenerate Cahn–Hilliard model for surface diffusion

Abstract

In this paper, we study the weak solutions of a modified degenerate Cahn–Hilliard type model for surface diffusion. With degenerate phase-dependent diffusion mobility and additional stabilizing function, this model is able to give the correct sharp interface limit. We introduce a notion of weak solutions for the nonlinear model. The existence of such solutions is obtained by approximations of the proposed model with non-degenerate mobilities. We also employ this method to prove the existence of weak solutions to a related model where the chemical potential contains a nonlocal term originating from self-climb of dislocations in crystalline materials.