 |
|
|
|
| HAL : hal-00461361, version 1 |
| arXiv : 1003.1059 |
| Fiche détaillée |  Récupérer au format |
|
|
|
|
| Viscosity solutions for a polymer crystal growth model |
|
|
| Pierre Cardaliaguet 1Olivier Ley 2 |
|
|
| (04/03/2010) |
|
|
|
| We prove existence of a solution for a polymer crystal growth model describing the movement of a front $(\Gamma(t))$ evolving with a nonlocal velocity. In this model the nonlocal velocity is linked to the solution of a heat equation with source $\delta_\Gamma$. The proof relies on new regularity results for the eikonal equation, in which the velocity is positive but merely measurable in time and with H\"{o}lder bounds in space. From this result, we deduce \textit{a priori} regularity for the front. On the other hand, under this regularity assumption, we prove bounds and regularity estimates for the solution of the heat equation. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire de mathématiques de Brest (LM) |
|
|
|
CNRS : UMR6205 – Université de Bretagne Occidentale - Brest – Institut Supérieur des Sciences et Technologies de Brest (ISSTB) |
|
|
| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
|
|
|
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
|
|
|
|
|
|
|
|
|
| Analyse numérique |
|
|
|
|
| Domaine | : | Mathématiques/Equations aux dérivées partielles |
|
|
| Nonlocal Hamilton-Jacobi Equations – nonlocal front propagation – level-set approach – geometrical properties – lower-bound gradient estimate – viscosity solutions – eikonal equation – heat equation. |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00461361, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00461361 | |
| oai:hal.archives-ouvertes.fr:hal-00461361 | |
| Contributeur : Olivier Ley | |
| Soumis le : Jeudi 4 Mars 2010, 14:51:09 | |
| Dernière modification le : Mardi 23 Mars 2010, 14:00:42 | |
