Existence of solutions to the Cahn-Hilliard/Allen-Cahn equation with degenerate mobility

Abstract

This article we study the Cahn-Hilliard/Allen-Cahn equation with degenerate mobility. Under suitable assumptions on the degenerate mobility and the double well potential, we prove existence of weak solutions, which can be obtained by considering the limits of Cahn-Hilliard/Allen-Cahn equations with non-degenerate mobility.

Keywords

• Cahn-Hilliard/Allen-Cahn equation
• existence
• Galerkin method
• degenerate mobility