Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis

Tong Li, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

68 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)1310-1333
Number of pages24
JournalJournal of Differential Equations
Volume250
Issue number3
DOIs
Publication statusPublished - 1 Feb 2011

Keywords

  • Chemotaxis
  • Conservation law
  • Energy estimates
  • Keller-Segel model
  • Large amplitude
  • Nonlinear stability
  • Traveling waves

ASJC Scopus subject areas

  • Analysis

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