American Institute of Mathematical Sciences

June  2016, 9(3): 759-775. doi: 10.3934/dcdss.2016027

Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions

 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 Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, 86962 Chasseneuil Futuroscope Cedex

Received  March 2015 Revised  April 2015 Published  April 2016

Our aim in this paper is to prove the existence and uniqueness of solutions to Cahn-Hilliard and Allen-Cahn type equations based on a modification of the Ginzburg-Landau free energy proposed in [12] (see also [16]) which takes into account strong anisotropy effects. In particular, the free energy contains a regularization term, called Willmore regularization.
Citation: Ahmad Makki, Alain Miranville. Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 759-775. doi: 10.3934/dcdss.2016027
References:

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References:
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