Phasefield theory for fractional diffusion-reaction equations and applications

Abstract : This paper is concerned with diffusion-reaction equations where the classical diffusion term, such as the Laplacian operator, is replaced with a singular integral term, such as the fractional Laplacian operator. As far as the reaction term is concerned, we consider bistable non-linearities. After properly rescaling (in time and space) these integro-differential evolution equations, we show that the limits of their solutions as the scaling parameter goes to zero exhibit interfaces moving by anisotropic mean curvature. The singularity and the unbounded support of the potential at stake are both the novelty and the challenging difficulty of this work.
Type de document :
Pré-publication, Document de travail
41 pages. 2009
Liste complète des métadonnées

Littérature citée [23 références]  Voir  Masquer  Télécharger
Contributeur : Cyril Imbert <>
Soumis le : vendredi 31 juillet 2009 - 14:32:36
Dernière modification le : jeudi 11 janvier 2018 - 06:12:20
Document(s) archivé(s) le : mardi 15 juin 2010 - 21:54:54


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-00408680, version 1
  • ARXIV : 0907.5524



Cyril Imbert, Panagiotis Souganidis. Phasefield theory for fractional diffusion-reaction equations and applications. 41 pages. 2009. 〈hal-00408680〉



Consultations de la notice


Téléchargements de fichiers