The existence of weak solutions for a nonlocal Cahn-Hilliard equation with degenerate mobility

Abstract

The aim of this paper is to study the existence of weak solutions for a nonlocal Cahn-Hilliard equations with degenerate mobility. Based on the uniform Schauder estimates and using the method of continuity, we obtain the existence of classical solutions for non-degenerate problems. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.