EXISTENCE OF SOLUTIONS FOR A ONE-DIMENSIONAL ALLEN-CAHN EQUATION | Zendy

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EXISTENCE OF SOLUTIONS FOR A ONE-DIMENSIONAL ALLEN-CAHN EQUATION

Author(s) -

Alain Miranville

Publication year - 2013

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2013019

Subject(s) - allen–cahn equation , uniqueness , regularization (linguistics) , cahn–hilliard equation , mathematics , willmore energy , anisotropy , mathematical analysis , mathematical physics , physics , differential equation , computer science , geometry , quantum mechanics , artificial intelligence , mean curvature , curvature , center of curvature

Our aim in this paper is to prove the existence and uniqueness of solutionsfor a one-dimensional Allen-Cahn type equation based on a modication of the Ginzburg-Landau free energy proposed in [9]. In particular, the free energy contains an additionalterm called Willmore regularization and takes into account anisotropy eects.

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