Global well-posedness and stability of constant equilibria in parabolic-elliptic chemotaxis systems without gradient sensing

Jaewook Ahn, Changwook Yoon

Research output: Contribution to journalArticlepeer-review

96 Scopus citations

Abstract

This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis {equation presented} in a smoothly bounded domain Ω Rn, n ≥ 1, under no-flux boundary conditions. The system contains a Fokker-Planck type diffusion with a motility function &gama;(v) = v-k , k > 0. The global existence of the unique bounded classical solutions is established without smallness of the initial data neither the convexity of the domain when n {equation presented} In addition, we find the conditions on parameters, k and ϵ, that make the spatially homogeneous equilibrium solution globally stable or linearly unstable.

Original languageEnglish
Pages (from-to)1327-1351
Number of pages25
JournalNonlinearity
Volume32
Issue number4
DOIs
StatePublished - 12 Mar 2019

Keywords

  • chemotaxis
  • global existence
  • Lyapunov functional
  • motility function

Fingerprint

Dive into the research topics of 'Global well-posedness and stability of constant equilibria in parabolic-elliptic chemotaxis systems without gradient sensing'. Together they form a unique fingerprint.

Cite this