Kinetic Models for Chemotaxis and their Drift-Diffusion Limits |
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Authors: | Fabio A C C Chalub Peter A Markowich Benoît Perthame Christian Schmeiser |
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Institution: | (1) Universität Wien, Austria;(2) École Normale Supérieure, Paris, France;(3) Technische Universität Wien, Austria |
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Abstract: | Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal |
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Keywords: | 2000 Mathematics Subject Classification: 92B05 82B40 |
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