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

Ahmad  Makki; Alain Miranville

doi:10.3934/dcdss.2016027

Article Contents

2016, Volume 9, Issue 3: 759-775. Doi: 10.3934/dcdss.2016027

This issue Previous Article Observability of $N$-dimensional integro-differential systems Next Article Semigroup-theoretic approach to identification of linear diffusion coefficients

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

Ahmad Makki^1, and
Alain Miranville^2,

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
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: February 28, 2015

Revised: March 31, 2015

Published: May 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B45; Secondary: 35K55.

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References

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