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Kinetic and Related Models (KRM)
 

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

Pages: 29 - 48, Volume 1, Issue 1, March 2008      doi:10.3934/krm.2008.1.29

 
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Nikolaos Bournaveas - University of Edinburgh, School of Mathematics, JCMB, King's Buildings, Edinburgh EH9 3JZ, United Kingdom (email)
Vincent Calvez - École Normale Supérieure, Département de Mathématiques et Applications, 45 rue d'Ulm, F 75230, Paris, cedex 05, France (email)

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.

Keywords:  kinetic model, bacterial motion, chemotaxis, dispersion estimates, Strichartz estimates, internal variables.
Mathematics Subject Classification:  Primary: 92C17, 82C40; Secondary: 35Q80, 92B05.

Received: November 2007;      Revised: November 2007;      Available Online: February 2008.