

Preprint 3/2003
From 1970 until present: the Keller-Segel model in chemotaxis and its consequences
Dirk Horstmann
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Submission date: 10. Jan. 2003
Pages: 53
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung, 105 (2003) 3, p. 103-165
Bibtex
MSC-Numbers: 35B30, 35J20, 35J65, 35K50, 35K50, 92C17
Keywords and phrases: chemotaxis equations, steady state analysis, global existence, global existence, global existence, self-similar solutions, traveling waves
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Abstract:
This article summarites various aspects and results for some general
formulations of the classical chemotaxis models also known as Keller-Segel
models. It is intended as a survey of results for the most common
formulation of this classical model for positive chemotactical movement
and offers possible generalizations of these results to more universal
models. Furthermore it collects open questions and outlines mathematical
progress in the study of the Keller-Segel model since the first
presentation of the equations in 1970.