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| HAL: hal-00452241, version 1 |
| arXiv: 1002.0326 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-02-01) | v2 (2010-07-12) | v3 (2011-07-16) |
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| Spirals moving by mean curvature. Part I: a comparison principle |
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| Nicolas Forcadel 1Cyril Imbert 1 |
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| (2010-02-01) |
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| In this paper, we study the motion of spirals by mean curvature in a (two dimensional) plane. Our motivation comes from dislocation dynamics; in this context, spirals appear when a screw dislocation line attains the surface of a crystal. The main result of this paper is a comparison principle for the corresponding quasi-linear equation. As far as motion of spirals are concerned, the novelty and originality of our setting and results come from the fact that, first, the singularity generated by the fixed point of spirals is taken into account for the first time (to the best of our knowledge), and second, spirals are studied in the whole space. We also prove that the Cauchy problem is well-posed by using Perron's method. |
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| 1: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 2: | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| Subject | : | Mathematics/Analysis of PDEs |
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| spirals – motion of interfaces – comparison principle – quasi-linear parabolic equation – viscosity solution |
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| hal-00452241, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00452241 | |
| oai:hal.archives-ouvertes.fr:hal-00452241 | |
| From: Cyril Imbert | |
| Submitted on: Monday, 1 February 2010 18:23:57 | |
| Updated on: Monday, 1 February 2010 21:40:59 | |
