Variational characterization of interior interfaces in phase transition models on convex plane domains
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 intersect...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2003-10-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/101/abstr.html |
| _version_ | 1819027257862127616 |
|---|---|
| author | Clara E. Garza-Hume Pablo Padilla |
| author_facet | Clara E. Garza-Hume Pablo Padilla |
| author_sort | Clara E. Garza-Hume |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T05:39:36Z |
| format | Article |
| id | doaj.art-3ed41f7efbad4e3690e1232d8f020999 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T05:39:36Z |
| publishDate | 2003-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3ed41f7efbad4e3690e1232d8f0209992022-12-21T19:14:18ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-10-01200310116Variational characterization of interior interfaces in phase transition models on convex plane domainsClara E. Garza-HumePablo PadillaWe 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.http://ejde.math.txstate.edu/Volumes/2003/101/abstr.htmlPhase transitionsingularly perturbed Allen-Cahn equationconvex plane domainvariational methodstransition layerGauss mapgeodesicvarifold. |
| spellingShingle | Clara E. Garza-Hume Pablo Padilla Variational characterization of interior interfaces in phase transition models on convex plane domains Electronic Journal of Differential Equations Phase transition singularly perturbed Allen-Cahn equation convex plane domain variational methods transition layer Gauss map geodesic varifold. |
| title | Variational characterization of interior interfaces in phase transition models on convex plane domains |
| title_full | Variational characterization of interior interfaces in phase transition models on convex plane domains |
| title_fullStr | Variational characterization of interior interfaces in phase transition models on convex plane domains |
| title_full_unstemmed | Variational characterization of interior interfaces in phase transition models on convex plane domains |
| title_short | Variational characterization of interior interfaces in phase transition models on convex plane domains |
| title_sort | variational characterization of interior interfaces in phase transition models on convex plane domains |
| topic | Phase transition singularly perturbed Allen-Cahn equation convex plane domain variational methods transition layer Gauss map geodesic varifold. |
| url | http://ejde.math.txstate.edu/Volumes/2003/101/abstr.html |
| work_keys_str_mv | AT claraegarzahume variationalcharacterizationofinteriorinterfacesinphasetransitionmodelsonconvexplanedomains AT pablopadilla variationalcharacterizationofinteriorinterfacesinphasetransitionmodelsonconvexplanedomains |