An Allen–Cahn equation based on an unconstrained order parameter and its Cahn–Hilliard limit

Abstract Our aim in this paper is to study an Allen–Cahn model based on a microforce balance and an unconstrained order parameter. We obtain the existence, uniqueness and regularity of solutions and prove that the solutions converge to those to the original Cahn–Hilliard equation on finite time intervals as a small parameter goes to zero.