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.