Nonlinear stability of large amplitude viscous shock waves of a generalized hyperbolicparabolic system arising in chemotaxis

Tong Li, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

54 Citations (Scopus)

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 languageEnglish
Pages (from-to)1967-1998
Number of pages32
JournalMathematical Models and Methods in Applied Sciences
Volume20
Issue number11
DOIs
Publication statusPublished - 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

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