PORTUGALIAEMATHEMATICA
Vol. 63, No. 2, pp. 227-250 (2006)
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PORTUGALIAE MATHEMATICA Vol. 63, No. 2, pp. 227-250 (2006) |
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A class of kinetic models for chemotaxis with threshold to prevent overcrowdingFabio A.C.C. Chalub and José Francisco RodriguesCentro 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. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2006 Sociedade Portuguesa de Matemática
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