Global existence for the kinetic chemotaxis model without pointwise memory effects, and including internal variables

Nikolaos Bournaveas; Vincent Calvez

doi:10.3934/krm.2008.1.29

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2008, Volume 1, Issue 1: 29-48. Doi: 10.3934/krm.2008.1.29

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Global existence for the kinetic chemotaxis model without pointwise memory effects, and including internal variables

Nikolaos Bournaveas^1, and
Vincent Calvez^2,

1.
University of Edinburgh, School of Mathematics, JCMB, King's Buildings, Edinburgh EH9 3JZ
2.
École Normale Supérieure, Département de Mathématiques et Applications, 45 rue d'Ulm, F 75230, Paris, cedex 05

Received: October 31, 2007

Revised: October 31, 2007

Published: February 2008

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Abstract

This paper is concerned with the kinetic model of Othmer-Dunbar-Alt for bacterial motion. Following a previous work, we apply the dispersion and Strichartz estimates to prove global existence under several borderline growth assumptions on the turning kernel. In particular we study the kinetic model with internal variables taking into account the complex molecular network inside the cell.

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Mathematics Subject Classification: Primary: 92C17, 82C40; Secondary: 35Q80, 92B05.

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