Long-term behaviour in a parabolic–elliptic chemotaxis–consumption model

Mario Fuest, Johannes Lankeit, Masaaki Mizukami

Research output: Contribution to journalArticle


Global existence and boundedness of classical solutions of the chemotaxis–consumption system nt=Δn−∇⋅(n∇c),0=Δc−nc, under no-flux boundary conditions for n and Robin-type boundary conditions ∂νc=(γ−c)g for c (with γ>0 and C1+β(∂Ω)∋g>0 for some β∈(0,1)) are established in bounded domains Ω⊂RN, N≥1. Under a smallness condition on γ, moreover, we show convergence to the stationary solution.

Original languageEnglish
Pages (from-to)254-279
Number of pages26
JournalJournal of Differential Equations
Publication statusPublished - 15 Jan 2021


  • Boundedness
  • Chemotaxis
  • Chemotaxis–consumption
  • Global existence
  • Large-time behaviour
  • Realistic oxygen boundary conditions

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