[Propagation dans les equations de type Fisher–KPP avec diffusion fractionnaire en milieux périodiques]
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.
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.
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@article{CRMATH_2012__350_19-20_885_0,
author = {Xavier Cabr\'e and Anne-Charline Coulon and Jean-Michel Roquejoffre},
title = {Propagation in {Fisher{\textendash}KPP} type equations with fractional diffusion in periodic media},
journal = {Comptes Rendus. Math\'ematique},
pages = {885--890},
publisher = {Elsevier},
volume = {350},
number = {19-20},
year = {2012},
doi = {10.1016/j.crma.2012.10.007},
language = {en},
}
TY - JOUR AU - Xavier Cabré AU - Anne-Charline Coulon AU - Jean-Michel Roquejoffre TI - Propagation in Fisher–KPP type equations with fractional diffusion in periodic media JO - Comptes Rendus. Mathématique PY - 2012 SP - 885 EP - 890 VL - 350 IS - 19-20 PB - Elsevier DO - 10.1016/j.crma.2012.10.007 LA - en ID - CRMATH_2012__350_19-20_885_0 ER -
%0 Journal Article %A Xavier Cabré %A Anne-Charline Coulon %A Jean-Michel Roquejoffre %T Propagation in Fisher–KPP type equations with fractional diffusion in periodic media %J Comptes Rendus. Mathématique %D 2012 %P 885-890 %V 350 %N 19-20 %I Elsevier %R 10.1016/j.crma.2012.10.007 %G en %F CRMATH_2012__350_19-20_885_0
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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