期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 250, 期 3, 页码 1310-1333出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2010.09.020
关键词
Keller-Segel model; Chemotaxis; Nonlinear stability; Traveling waves; Conservation law; Large amplitude; Energy estimates
类别
资金
- Hong Kong Polytechnic University
- Vanderbilt University
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.
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