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

Hyung Ju Hwang, Kyungkeun Kang, and Angela Stevens

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Submission date: 03. Mar. 2003
Pages: 15
published in: Discrete and continuous dynamical systems / B, 5 (2005) 2, p. 319-334 
DOI number (of the published article): 10.3934/dcdsb.2005.5.319
Bibtex
MSC-Numbers: 35K55, 45K05, 82C70, 92C17
Keywords and phrases: chemotaxis, kinetic model, drift-diffusion limit, global existence
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Abstract:
We study a kinetic model for chemotaxis introduced by Othmer, Dunbar, and Alt [J. Math. Biol. 26 (1988) no. 3, 263--298], which was motivated by earlier results of Alt, presented in [J. Math. Biol. 9 (1980) 147--177, J. Reine Angew. Math. 322 (1981), 15--41]. 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 [ANUM preprint 4/02, ANUM preprint 14/02]. 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.