Existence of periodic solution for a Cahn-Hilliard/Allen-Cahn equation in two space dimensions
Changchun Liu Hui Tang
Evolution Equations & Control Theory 2017, 6(2): 219-237 doi: 10.3934/eect.2017012

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.

keywords: Cahn-Hilliard/Allen-Cahn equation existence uniqueness periodic solution

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