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Asymptotic stability of a composite wave of two traveling waves to a hyperbolic–parabolic system modeling chemotaxis
Author(s) -
Li Jingyu,
Wang Lina,
Zhang Kaijun
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2731
Subject(s) - mathematics , mathematical analysis , exponential stability , stability (learning theory) , chemotaxis , traveling wave , boundary (topology) , zero (linguistics) , boundary value problem , stability theory , physics , biochemistry , chemistry , linguistics , philosophy , computer science , receptor , quantum mechanics , nonlinear system , machine learning
In this paper, we study the asymptotic stability of a composite wave consisting of two traveling waves to a hyperbolic–parabolic system modeling repulsive chemotaxis. On the basis of elementary energy estimates, we show that the composite wave is asymptotically stable under general initial perturbations, which are not necessarily zero integral. As an application, we obtain a similar result for this system in the presence of a boundary. Copyright © 2013 John Wiley & Sons, Ltd.