Existence and instability of traveling pulses of Keller-Segel system with nonlinear chemical gradients and small diffusions

Chueh Hsin Chang, Yu Shuo Chen, John M. Hong, Bo Chih Huang

Research output: Contribution to journalArticlepeer-review

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Abstract

In this paper, we consider a generalized model of 2 × 2 KellerSegel system with a nonlinear chemical gradient and small cell diffusion. The existence of the traveling pulses for such equations is established by the methods of geometric singular perturbation (GSP) and trapping regions from dynamical systems theory. By the technique of GSP, we show that the necessary condition for the existence of traveling pulses is that their limiting profiles with vanishing diffusion can only consist of the slow flows on the critical manifold of the corresponding algebraic-differential system. We also consider the linear instability of these pulses by the spectral analysis of the linearized operators.

Original languageEnglish
Pages (from-to)143-167
Number of pages25
JournalNonlinearity
Volume32
Issue number1
DOIs
StatePublished - Jan 2019

Keywords

  • geometric singular perturbation theory
  • Keller-Segle model
  • linear stability
  • spectral theory
  • traveling wave solution

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