Abstract
Traveling wave (band) behavior driven by chemotaxis was observed experimentally by Adler1,2and was modeled by Keller and Segel.15For a quasilinear hyperbolicparabolic system that arises as a non-diffusive limit of the KellerSegel 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.
Original language | English |
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Pages (from-to) | 1967-1998 |
Number of pages | 32 |
Journal | Mathematical Models and Methods in Applied Sciences |
Volume | 20 |
Issue number | 11 |
DOIs | |
Publication status | Published - 1 Nov 2010 |
Keywords
- chemotaxis
- energy estimates
- large amplitude
- non-diffusive signals
- Nonlinear conservation laws
- nonlinear kinetics
- nonlinear stability
- ShizutaKawashima condition
- traveling waves
ASJC Scopus subject areas
- Modelling and Simulation
- Applied Mathematics