Evolution Equations and Control Theory (EECT)

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

Pages: 219 - 237, Volume 6, Issue 2, June 2017      doi:10.3934/eect.2017012

       Abstract        References        Full Text (368.5K)       Related Articles       

Changchun Liu - Department of Mathematics, Jilin University, Changchun 130012, China (email)
Hui Tang - School of Science, Changchun University, Changchun 130022, China (email)

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.

Keywords:  Cahn-Hilliard/Allen-Cahn equation, existence, uniqueness, periodic solution.
Mathematics Subject Classification:  Primary: 35B10, 35K25; Secondary: 35K55.

Received: June 2015;      Revised: July 2016;      Available Online: April 2017.