Stability of traveling waves of the Keller-Segel system with logarithmic sensitivity

Jingyu Li, Tong Li, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

36 Citations (Scopus)

Abstract

Proceeding with a series of works (Refs. 12, 23-25) by the authors, this paper establishes the nonlinear asymptotic stability of traveling wave solutions of the Keller-Segel system with nonzero chemical diffusion and linear consumption rate, where the right asymptotic state of cell density is vacuum (zero) and the initial value is a perturbation with zero integral from the spatially shifted traveling wave. The main challenge of the problem is various singularities caused by the logarithmic sensitivity and the vacuum asymptotic state, which are overcome by a Hopf-Cole type transformation and the weighted energy estimates with an unbounded weight function introduced in the paper.
Original languageEnglish
Pages (from-to)2819-2849
Number of pages31
JournalMathematical Models and Methods in Applied Sciences
Volume24
Issue number14
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Chemotaxis
  • Nonlinear stability
  • Traveling waves
  • Vacuum state
  • Weighted energy estimates

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

Cite this