Existence and diffusive limit of a two-species kinetic model of chemotaxis

Casimir Emako; Luís Neves de Almeida; Nicolas Vauchelet

doi:10.3934/krm.2015.8.359

Article Contents

2015, Volume 8, Issue 2: 359-380. Doi: 10.3934/krm.2015.8.359

This issue Previous Article Compressible Euler equations interacting with incompressible flow Next Article Galactic dynamics in MOND---Existence of equilibria with finite mass and compact support

Existence and diffusive limit of a two-species kinetic model of chemotaxis

1.
Sorbonne Universites, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris
2.
Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris

Received: March 31, 2014

Revised: December 31, 2014

Published: May 2015

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Abstract

In this paper, we propose a kinetic model describing the collective motion by chemotaxis of two species in interaction emitting the same chemoattractant. Such model can be seen as a generalisation to several species of the Othmer-Dunbar-Alt model which takes into account the run-and-tumble process of bacteria. Existence of weak solutions for this two-species kinetic model is studied and the convergence of its diffusive limit towards a macroscopic model of Keller-Segel type is analysed.

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Mathematics Subject Classification: 35K55, 45K05, 82C70, 92C17.

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References

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