On an anisotropic Allen-Cahn system

Alain Miranville

doi:10.4067/S0719-06462015000200005

On an anisotropic Allen-Cahn system

Authors

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

DOI:

https://doi.org/10.4067/S0719-06462015000200005

Keywords:

Allen-Cahn equation, Willmore regularization, anisotropy effects, well-posedness

Abstract

Our aim in this paper is to prove the existence and uniqueness of solutions for an Allen-Cahn type system based on a modification of the Ginzburg-Landau free energy proposed in [11]. In particular, the free energy contains an additional term called Willmore regularization and takes into account anisotropy effects.