Phase transitions and bump solutions of the keller-segel model with volume exclusion

Jose A. Carrillo, Xinfu Chen, Qi Wang, Zhian Wang, Lu Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


We show that the Keller-Segel model in one dimension with Neumann boundary conditions and quadratic cellular diffusion has an intricate phase transition diagram depending on the chemosensitivity strength. Explicit computations allow us to find a myriad of symmetric and asymmetric stationary states whose stability properties are mostly studied via free energy decreasing numerical schemes. The metastability behavior and staircased free energy decay are also illustrated via these numerical simulations.

Original languageEnglish
Pages (from-to)232-261
Number of pages30
JournalSIAM Journal on Applied Mathematics
Issue number1
Publication statusPublished - 16 Jan 2020


  • Bifurcation
  • Bump solution
  • Degenerate diffusion
  • Keller-Segel
  • Phase transition

ASJC Scopus subject areas

  • Applied Mathematics

Cite this