Convergence to traveling waves of a singular PDE-ODE hybrid chemotaxis system in the half space

Jingyu Li, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper is concerned with the asymptotic stability of the initial-boundary value problem of a singular PDE-ODE hybrid chemotaxis system in the half space R+=[0,∞). We show that when the non-zero flux boundary condition at x=0 is prescribed and the initial data are suitably chosen, the solution of the initial-boundary value problem converges, as time tend to infinity, to a shifted traveling wavefront restricted in the half space [0,∞) where the wave profile and speed are uniquely selected by the boundary flux data. The results are proved by a Cole-Hopf type transformation and weighted energy estimates along with the technique of taking the anti-derivative.

Original languageEnglish
Pages (from-to)6940-6970
Number of pages31
JournalJournal of Differential Equations
Volume268
Issue number11
DOIs
Publication statusPublished - 15 May 2020

Keywords

  • Boundary layer effect
  • Convergence
  • Half space
  • Shifted traveling waves
  • Singular chemotaxis

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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