The fractional diffusion limit of a kinetic model with biochemical pathway

Abstract : Kinetic-transport equations that take into account the intra-cellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intra-cellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then, comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

Littérature citée [26 références]  Voir  Masquer  Télécharger

https://hal.sorbonne-universite.fr/hal-01584754
Contributeur : Benoît Perthame <>
Soumis le : samedi 9 septembre 2017 - 15:02:24
Dernière modification le : jeudi 26 avril 2018 - 10:28:43

Fichiers

Fractional-noise_F.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01584754, version 1
  • ARXIV : 1709.03308

Collections

Citation

Benoît Perthame, Weiran Sun, Min Tang. The fractional diffusion limit of a kinetic model with biochemical pathway. 2017. 〈hal-01584754〉

Partager

Métriques

Consultations de la notice

319

Téléchargements de fichiers

60