Aggregated steady states of a kinetic model for chemotaxis

Anne Nouri; Christian Schmeiser

doi:10.3934/krm.2017013

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2017, Volume 10, Issue 1: 313-327. Doi: 10.3934/krm.2017013

This issue Previous Article On interfaces between cell populations with different mobilities Next Article

Aggregated steady states of a kinetic model for chemotaxis

Anne Nouri^1, , and
Christian Schmeiser^2,

1.
Aix-Marseille University, CNRS, Centrale Marseille, I2M UMR 7373, 13453 Marseille, France
2.
University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

Received: December 31, 2015

Revised: June 30, 2016

Published: September 2017

The second author is supported by the Austrian Science Fund grant no. W1245.

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Abstract

A kinetic chemotaxis model with attractive interaction by quasistationary chemical signalling is considered. The special choice of the turning operator, with velocity jumps biased towards the chemical concentration gradient, permits closed ODE systems for moments of the distribution function of arbitrary order. The system for second order moments exhibits a critical mass phenomeneon. The main result is existence of an aggregated steady state for supercritical mass.

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Mathematics Subject Classification: Primary: 35Q20, 92C17.

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References

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