Nonlinear Stability of Large Amplitude Viscous Shock Waves of a Generalized Hyperbolic{parabolic System Arising in Chemotaxis

@inproceedings{Wang2010NonlinearSO,
  title={Nonlinear Stability of Large Amplitude Viscous Shock Waves of a Generalized Hyperbolic\{parabolic System Arising in Chemotaxis},
  author={Z Wang},
  year={2010}
}
Traveling wave (band) behavior driven by chemotaxis was observed experimentally by Adler and was modeled by Keller and Segel. For a quasilinear hyperbolic parabolic system that arises as a non-di®usive 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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