Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 63, No. 2, pp. 227-250 (2006)

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A class of kinetic models for chemotaxis with threshold to prevent overcrowding

Fabio A.C.C. Chalub and José Francisco Rodrigues

Centro de Matemática e Aplicaç\ oes Fundamentais, Universidade de Lisboa,
Av. Prof. Gama Pinto 2, P-1649-003, Lisboa -- PORTUGAL
E-mail: chalub@cii.fc.ul.pt
Centro de Matemática da Universidade de Coimbra,
and FCUL/Universidade de Lisboa, c/o CMAF,
Av. Prof. Gama Pinto 2, P-1649-003, Lisboa -- PORTUGAL
E-mail: rodrigue@fc.ul.pt

Abstract: We introduce three new examples of kinetic models for chemotaxis, where a kinetic equation for the phase-space density is coupled to a parabolic or elliptic equation for the chemo-attractant, in two or three dimensions. We prove that these models have global-in-time existence and rigorously converge, in the drift-diffusion limit to the Keller--Segel model. Furthermore, the cell density is uniformly-in-time bounded. This implies, in particular, that the limit model also has global existence of solutions.

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Electronic version published on: 7 Mar 2008.

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