Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity

Hai Yang Jin, Jingyu Li, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

54 Citations (Scopus)

Abstract

This paper establishes the nonlinear stability of traveling wave solutions to a chemotaxis model with singular (or logarithmic) sensitivity and its transformed parabolic-hyperbolic system. Depending on the parameter signs, we discuss the linear instability of traveling wave solutions using the spectral analysis and nonlinear asymptotic stability of traveling wave solutions with zero end state by the weighted energy estimates, where the latter result solves the open question left in a previous work (Li and Wang, 2009 [7]).
Original languageEnglish
Pages (from-to)193-219
Number of pages27
JournalJournal of Differential Equations
Volume255
Issue number2
DOIs
Publication statusPublished - 15 Jul 2013

Keywords

  • Chemotaxis
  • Linear instability
  • Nonlinear stability
  • Traveling wave solutions
  • Weighted energy estimates

ASJC Scopus subject areas

  • Analysis

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