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Traveling waves for chemotaxis–systems
Author(s) -
Schwetlick Hartmut
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310508
Subject(s) - traveling wave , logarithm , chemotaxis , monotone polygon , range (aeronautics) , pulse (music) , population , statistical physics , physics , mathematical analysis , mathematics , chemistry , materials science , quantum mechanics , geometry , biochemistry , receptor , demography , voltage , sociology , composite material
In this paper we study the existence of traveling wave solutions to the Keller‐Segel model, a general model of chemotaxis, where the species do not reproduce. In the case of logarithmic sensitivity we show that various functionals modeling the reactive feedback on the chemo‐attractant do allow for traveling waves and a wide range of qualitatively different behavior is possible. We can find monotone fronts as well as pulse solutions in the densities of the population and the chemical. In particular, a new kind of solution exists, where both densities travel as pulses.