Critical mass on the keller-segel system with signal-dependent motility

Hai Yang Jin, Zhi An Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

60 Citations (Scopus)


This paper is concerned with the global boundedness and blowup of solutions to the Keller-Segel system with density-dependent motility in a two-dimensional bounded smooth domain with Neumman boundary conditions. We show that if the motility function decays exponentially, then a critical mass phenomenon similar to the minimal Keller-Segel model will arise. That is, there is a number m > 0, such that the solution will globally exist with uniform-in-time bound if the initial cell mass (i.e., L1-norm of the initial value of cell density) is less than m, while the solution may blow up if the initial cell mass is greater than m

Original languageEnglish
Pages (from-to)4855-4873
Number of pages19
JournalProceedings of the American Mathematical Society
Issue number11
Publication statusPublished - Nov 2020


  • Blow-up
  • Critical mass
  • Global existence
  • Signal-dependent motility

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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