Electron. J. Differential Equations, Vol. 2016 (2016), No. 329, pp. 1-22.

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

Xiaoli Zhang, Changchun Liu

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.

Submitted September 2, 2016. Published December 24, 2016.
Math Subject Classifications: 35G25, 35K55, 35K65.
Key Words: Cahn-Hilliard/Allen-Cahn equation; existence; Galerkin method; degenerate mobility.

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Xiaoli Zhang
Department of Mathematics
Jilin University
Changchun 130012, China
email: mathche@sina.com
Changchun Liu
Department of Mathematics
Jilin University
Changchun 130012, China
email: liucc@jlu.edu.cn

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