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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
19/2003

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

Hyung Ju Hwang, Kyungkeun Kang and Angela Stevens

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.

Received:
Mar 3, 2003
Published:
Mar 3, 2003
MSC Codes:
35K55, 45K05, 82C70, 92C17
Keywords:
chemotaxis, kinetic model, drift-diffusion limit, global existence

Related publications

inJournal
2005 Repository Open Access
Hyung Ju Hwang, Kyungkeun Kang and Angela Stevens

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

In: Discrete and continuous dynamical systems / B, 5 (2005) 2, pp. 319-334