# American Institute of Mathematical Sciences

August  2019, 24(8): 3633-3651. doi: 10.3934/dcdsb.2018308

## On the Cahn-Hilliard/Allen-Cahn equations with singular potentials

 1 Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France 2 Xiamen University, School of Mathematical Sciences, Xiamen, Fujian, China 3 Université Libanaise, Laboratoire de Mathématiques - EDST, Faculté des Sciences, Hadath, Liban

Received  February 2018 Revised  June 2018 Published  November 2018

The purpose of this work is to prove the existence and uniqueness of the solution for a Cahn-Hilliard/Allen-Cahn system with singular potentials (and, in particular, the thermodynamically relevant logarithmic potentials). We also prove the existence of the global attractor. Finally, we show further regularity results and we prove a strict separation property (from the pure states) in one space dimension.

Citation: Alain Miranville, Wafa Saoud, Raafat Talhouk. On the Cahn-Hilliard/Allen-Cahn equations with singular potentials. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3633-3651. doi: 10.3934/dcdsb.2018308
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##### References:
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