Comptes Rendus
Partial Differential Equations
Propagation in Fisher–KPP type equations with fractional diffusion in periodic media
Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 885-890.

We are interested in the time asymptotic location of the level sets of solutions to Fisher–KPP reaction–diffusion equations with fractional diffusion in periodic media. We show that the speed of propagation is exponential in time, with a precise exponent depending on a periodic principal eigenvalue, and that it does not depend on the space direction. This is in contrast with the Freidlin–Gärtner formula for the standard Laplacian.

On sʼintéresse ici à la localisation asymptotique en temps des lignes de niveaux des solutions dʼequations de réaction–diffusion de type Fisher–KPP avec diffusion fractionnaire en milieu périodique. Nous montrons que la vitesse de propagation est exponentielle en temps, avec un exposant dépendant dʼune valeur propre principale périodique, et que cette vitesse ne dépend pas de la direction de propagation. Ceci est en contraste avec la formule de Freidlin–Gärtner pour le laplacien standard.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.10.007
Xavier Cabré 1; Anne-Charline Coulon 2; Jean-Michel Roquejoffre 2

1 ICREA and Universitat Politècnica de Catalunya, Dep. de Matemàtica Aplicada I, Av. Diagonal 647, 08028 Barcelone, Spain
2 Institut de mathématiques, (UMR CNRS 5219), université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France
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Xavier Cabré; Anne-Charline Coulon; Jean-Michel Roquejoffre. Propagation in Fisher–KPP type equations with fractional diffusion in periodic media. Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 885-890. doi : 10.1016/j.crma.2012.10.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.007/

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