NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC-PARABOLIC SYSTEM ARISING IN CHEMOTAXIS

被引：79
|
作者：
Li, Tong [2 ]
Wang, Zhi-An [1 ]
机构：
[1] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2010年 / 20卷 / 11期
关键词：
Nonlinear conservation laws; nonlinear stability; chemotaxis; traveling waves; non-diffusive signals; large amplitude; nonlinear kinetics; energy estimates; Shizuta-Kawashima condition; TRAVELING-WAVES; MODEL; PROFILES; AGGREGATION; EQUATIONS; BANDS;
D O I：
10.1142/S0218202510004830
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Traveling wave (band) behavior driven by chemotaxis was observed experimentally by Adler(1,2) and was modeled by Keller and Segel.15 For a quasilinear hyperbolic parabolic system that arises as a non-diffusive limit of the Keller-Segel model with nonlinear kinetics, we establish the existence and nonlinear stability of traveling wave solutions with large amplitudes. The numerical simulations are performed to show the stability of the traveling waves under various perturbations.
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页码：1967 / 1998
页数：32
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