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| HAL : hal-00497492, version 1 |
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| Slow motion of particle systems as a limit of a reaction-diffusion equation with half-Laplacian in dimension one |
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| Régis Monneau 1Maria Del Mar Gonzalez 2 |
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| (05/07/2010) |
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| We consider a reaction-diffusion equation with a half-Laplacian. In the case where the solution is independent on time, the model reduces to the Peierls-Nabarro model describing dislocations as transition layers in a phase field setting. We introduce a suitable rescaling of the evolution equation, using a small parameter $\varepsilon$. As $\varepsilon$ goes to zero, we show that the limit dynamics is characterized by a system of ODEs describing the motion of particles with two-body interactions. The interaction forces are in $1/x$ and correspond to the well-known interaction between dislocations. |
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| 1 : | 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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| 2 : | Universitat Politècnica de Catalunya (UPC) |
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Universitat Politécnica de Catalunya |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00497492, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00497492 | |
| oai:hal.archives-ouvertes.fr:hal-00497492 | |
| Contributeur : Régis Monneau | |
| Soumis le : Lundi 5 Juillet 2010, 11:04:17 | |
| Dernière modification le : Lundi 5 Juillet 2010, 13:33:19 | |
