Variational characterization of interior interfaces in phase transition models on convex plane domains
Date
2003-10-02
Authors
Garza-Hume, Clara E.
Padilla, Pablo
Journal Title
Journal ISSN
Volume Title
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.
Rights
Attribution 4.0 International