Radial spiky steady states of a flux-limited Keller–Segel model: Existence, asymptotics, and stability

Zhi An Wang, Xin Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper is concerned with the radial stationary problem of a flux-limited Keller–Segel model derived in a multidimensional bounded domain with Neumann boundary conditions. With the global bifurcation theory and Helly compactness theorem by treating the chemotactic coefficient as a bifurcation parameter, we establish the existence of nonconstant monotone radial stationary solutions and further show that the radial stationary solution will tend to a Dirac delta mass as the chemotactic coefficient tends to infinity. By using the stability criterion of Crandall and Rabinnowitz, we prove the linearized stability of bifurcating stationary solutions near the bifurcation points.

Original languageEnglish
Pages (from-to)1251-1273
Number of pages23
JournalStudies in Applied Mathematics
Volume148
Issue number3
DOIs
Publication statusPublished - Apr 2022

Keywords

  • flux-limited Keller–Segel model
  • global bifurcation theory
  • Helly compactness theorem
  • linearized stability
  • stationary solutions

ASJC Scopus subject areas

  • Applied Mathematics

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