Well-posedness for  two types of generalized Keller-Segel system of chemotaxis in  critical Besov spaces

Zhichun Zhai

doi:10.3934/cpaa.2011.10.287

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2011, Volume 10, Issue 1: 287-308. Doi: 10.3934/cpaa.2011.10.287

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Well-posedness for two types of generalized Keller-Segel system of chemotaxis in critical Besov spaces

Zhichun Zhai^1,

1.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1

Received: December 31, 2009

Revised: April 30, 2010

Published: December 2010

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Abstract

In this paper, we study two types of generalized Keller-Segel system of chemotaxis. We establish the global existence and uniqueness of solutions to the semilinear Keller-Segel system of doubly parabolic type and the nonlinear nonlocal type Keller-Segel system with data in Besov spaces. Moreover, we prove the stability of solution to the first type. Our main tools are the $L^p-L^q$ estimates for $e^{-t(-\triangle)^{\theta/2}}$ in Besov spaces and the perturbation of linearization.

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Mathematics Subject Classification: Primary: 35K55, 35K15; Secondary: 92C17, 92B05.

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