Prevention of blow-up by fast diffusion in chemotaxis

Yung Sze Choi, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

38 Citations (Scopus)

Abstract

In this paper, we study a strongly coupled parabolic system with cross diffusion term which models chemotaxis. The diffusion coefficient goes to infinity when cell density tends to an allowable maximum value. Such 'fast diffusion' leads to global existence of solutions in bounded domains for any given initial data irrespective of the spatial dimension, which is usually the goal of many modifications to the classical Keller-Segel model. The key estimates that make this possible have been obtained by a technique that uses ideas from Moser's iterations.
Original languageEnglish
Pages (from-to)553-564
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume362
Issue number2
DOIs
Publication statusPublished - 15 Feb 2010
Externally publishedYes

Keywords

  • Blow-up
  • Chemotaxis
  • Fast diffusion
  • Global existence
  • Pattern formation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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