Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation

Masaaki Mizukami, Tatsuhiko Ono, Tomomi Yokota

Research output: Contribution to journalArticle

Abstract

This paper deals with the quasilinear degenerate chemotaxis system with flux limitation, [Formula presented] under no-flux boundary conditions in balls Ω⊂Rn, and the initial condition u|t=0=u0 for a radially symmetric and positive initial data u0∈C3(Ω‾), where χ>0 and [Formula presented]. Bellomo–Winkler [3] proved local existence of unique classical solutions and extensibility criterion ruling out gradient blow-up as well as global existence and boundedness of solutions when p=q=1 under some conditions for χ and ∫Ωu0. This paper derives local existence and extensibility criterion ruling out gradient blow-up when p,q≥1, and moreover shows global existence and boundedness of solutions when [Formula presented].

Original languageEnglish
Pages (from-to)5115-5164
Number of pages50
JournalJournal of Differential Equations
Volume267
Issue number9
DOIs
Publication statusPublished - 15 Oct 2019

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Keywords

  • Boundedness
  • Degenerate chemotaxis system
  • Extensibility criterion
  • Flux limitation

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