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May  2005, 5(2): 319-334. doi: 10.3934/dcdsb.2005.5.319

Drift-diffusion limits of kinetic models for chemotaxis: A generalization

H.J. Hwang 1, , K. Kang 1, and  A. Stevens 1,

1. 

Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22 - 26, D-04103 Leipzig, Germany, Germany, Germany

Received  June 2003 Revised  July 2004 Published  February 2005

We study a kinetic model for chemotaxis introduced by Othmer, Dunbar, and Alt [23], which was motivated by earlier results of Alt, presented in [1], [2]. In two papers by Chalub, Markowich, Perthame and Schmeiser, it was rigorously shown that, in three dimensions, this kinetic model leads to the classical Keller-Segel model as its drift-diffusion limit when the equation of the chemo-attractant is of elliptic type [4], [5]. As an extension of these works we prove that such kinetic models have a macroscopic diffusion limit in both two and three dimensions also when the equation of the chemo-attractant is of parabolic type, which is the original version of the chemotaxis model.
Keywords: global existence., chemotaxis, drift-diffusion limit, kinetic model.
Mathematics Subject Classification: 35K55, 45K05, 82C70, 92C1.
Citation: H.J. Hwang, K. Kang, A. Stevens. Drift-diffusion limits of kinetic models for chemotaxis: A generalization. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 319-334. doi: 10.3934/dcdsb.2005.5.319
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