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

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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… Click to show full abstract

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.

Keywords: order parameter; cahn hilliard; parameter; allen cahn; unconstrained order

Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2021

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