Variational characterization of interior interfaces in phase transition models on convex plane domains

Date

2003-10-02

Authors

Garza-Hume, Clara E.
Padilla, Pablo

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Publisher

Southwest Texas State University, Department of Mathematics

Abstract

We consider the singularly perturbed Allen-Cahn equation on a strictly convex plane domain. We show that when the perturbation parameter tends to zero there are solutions having a transition layer that tends to a straight line segment. This segment can be characterized as the shortest path intersecting the boundary orthogonally at two points.

Description

Keywords

Phase transitions, Singularly perturbed Allen-Cahn equation, Convex plane domain, Variational methods, Transition layer, Gauss map, Geodesic, Varifold

Citation

Garza-Hume, C. E., & Padilla, P. (2003). Variational characterization of interior interfaces in phase transition models on convex plane domains. <i>Electronic Journal of Differential Equations, 2003</i>(101), pp. 1-6.

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Attribution 4.0 International

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