Existence of periodic solution for a Cahn-Hilliard/Allen-Cahn equation in two space dimensions

Changchun Liu; Hui Tang

doi:10.3934/eect.2017012

Article Contents

2017, Volume 6, Issue 2: 219-237. Doi: 10.3934/eect.2017012

This issue Previous Article Optimal control for a hyperbolic problem in composites with imperfect interface: A memory effect Next Article General decay for a viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping, dynamic boundary conditions and a time-varying delay term

Existence of periodic solution for a Cahn-Hilliard/Allen-Cahn equation in two space dimensions

Changchun Liu^1, , and
Hui Tang^2,

1.
Department of Mathematics, Jilin University, Changchun 130012, China
2.
School of Science, Changchun University, Changchun 130022, China

* Corresponding author:Changchun Liu
* Corresponding author:Changchun Liu

Received: May 31, 2015

Revised: June 30, 2016

Published: May 2017

This work is supported by the Jilin Scientific and Technological Development Program (no. 20170101143JC) and the National Science Foundation of China (no. 11471164)

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Abstract

In this paper, we discuss the existence of the periodic solutions of a Cahn-Hillard/Allen-Cahn equation which is introduced as a simplification of multiple microscopic mechanisms model in cluster interface evolution. Based on the Schauder type a priori estimates, which here will be obtained by means of a modified Campanato space, we prove the existence of time-periodic solutions in two space dimensions. The uniqueness of solutions is also discussed.

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Mathematics Subject Classification: Primary: 35B10, 35K25; Secondary: 35K55.

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