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Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis
Journal article   Open access   Peer reviewed

Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis

Tong Li and Zhi-An Wang
Journal of Differential Equations, Vol.250(3), pp.1310-1333
02/01/2011
DOI: 10.1016/j.jde.2010.09.020
url
https://doi.org/10.1016/j.jde.2010.09.020View
Published (Version of record) Open Access

Abstract

In this paper, we establish the existence and the nonlinear stability of traveling wave solutions to a system of conservation laws which is transformed, by a change of variable, from the well-known Keller-Segel model describing cell (bacteria) movement toward the concentration gradient of the chemical that is consumed by the cells. We prove the existence of traveling fronts by the phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without the smallness assumption on the wave strengths by the method of energy estimates. (C) 2010 Elsevier Inc. All rights reserved.
Mathematics Physical Sciences Science & Technology

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