Higher-order anisotropic models in phase separation-Reference-Cited by-同舟云学术

Higher-order anisotropic models in phase separation

Published:2017-03-16 Issue:1 Volume:8 Page:278-302
ISSN:2191-9496
Container-title:Advances in Nonlinear Analysis
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Author:

Cherfils Laurence¹,Miranville Alain²,Peng Shuiran³

Affiliation:

1. LaSIE, Université de La Rochelle, Avenue Michel Crépeau, F-17042 La Rochelle Cedex, France

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

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

Abstract

Abstract Our aim in this paper is to study higher-order (in space) Allen–Cahn and Cahn–Hilliard models. In particular, we obtain well-posedness results, as well as the existence of the global attractor. We also give, for the Allen–Cahn models, numerical simulations which illustrate the effects of the higher-order terms and the anisotropy.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/downloadpdf/journals/anona/8/1/article-p278.xml

Reference92 articles.

1. Well-posedness and longtime behavior for the modified phase-field crystal equation;Math. Models Methods Appl. Sci.,2014

2. Estimates near the boundary for solutions of elliptic partial differential equations. I;Comm. Pure Appl. Math.,1959

3. Modelling and numerical simulations of dendritic crystal growth;Phys. D,1993

4. On the notion of ξ-vector and stress tensor for a general class of anisotropic diffuse interface models;Proc. R. Soc. Lond. Ser. A,1997

5. Mean curvature and weighted mean curvature;Acta Metall. Mater.,1992

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