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

Author: Wrzosek, Dariusz

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 136, Number 2, May 2006 , pp. 431-444(14)

Publisher: Royal Society of Edinburgh

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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.

Document Type: Research article

Publication date: 2006-05-01