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March  2008, 1(1): 29-48. doi: 10.3934/krm.2008.1.29

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, United Kingdom
2. 

École Normale Supérieure, Département de Mathématiques et Applications, 45 rue d'Ulm, F 75230, Paris, cedex 05, France

Received  November 2007 Revised  November 2007 Published  February 2008

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.
Keywords: chemotaxis, internal variables., dispersion estimates, bacterial motion, kinetic model, Strichartz estimates.
Mathematics Subject Classification: Primary: 92C17, 82C40; Secondary: 35Q80, 92B0.
Citation: Nikolaos Bournaveas, Vincent Calvez. Global existence for the kinetic chemotaxis model without pointwise memory effects, and including internal variables. Kinetic and Related Models, 2008, 1 (1) : 29-48. doi: 10.3934/krm.2008.1.29
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