Boundedness in a fully parabolic chemotaxis system with singular sensitivity

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77 Citations (Scopus)

Abstract

This paper deals with a fully parabolic chemotaxis system ut=δu-χ∇{dot operator}(uv∇v), vt=δv-v+u with singular sensitivity χv (χ. >. 0) on a bounded domain Ω⊂Rn, n≥. 2. The main result solves the open problem of uniform-in-time boundedness of solutions for χ<2n, which was conjectured by Winkler [16].

Original languageEnglish
Pages (from-to)675-684
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume424
Issue number1
DOIs
Publication statusPublished - 2015 Apr 1
Externally publishedYes

Keywords

  • Boundedness
  • Chemotaxis
  • Singular sensitivity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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