Singular limit of a degenerate chemotaxis-Fisher equation

Fathi Dkhil

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Submission date: 10. Mar. 2003
published in: Hiroshima mathematical journal, 34 (2004) 1, p. 101-115 
Bibtex
MSC-Numbers: 35K65, 35K45, 35K57, 35B50, 92C17
Keywords and phrases: reaction-diffusion system, chemotaxis, keller-segel model, travelling wave, inteface motion

Abstract:
We study the singular limit of an advection-reaction-degenerate-diffusion equation which appear in a chemotaxis model. We prove the convergence to the solution of a free boundary problem where the motion equation of the interface involve the gradient of the chemotactic concentration and the critical velocity of a degenerate Fisher equation.