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Long-time behaviour of solutions to a chemotaxis model with volume-filling effect

Published online by Cambridge University Press:  12 July 2007

Dariusz Wrzosek
Dariusz Wrzosek
Affiliation:
Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland (darekw@mimuw.edu.pl)
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Abstract

The Lyapunov functional is constructed for a quasilinear parabolic system which models chemotaxis and takes into account a volume-filling effect. For some typical case it is proved that the ω-limit set of any trajectory consists of regular stationary solutions. Some lower and upper bounds on the stationary solutions are found. For a given range of parameters there are stationary solutions which are inhomogeneous in space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 2 , April 2006 , pp. 431 - 444
Copyright
Copyright © Royal Society of Edinburgh 2006

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