Global existence and boundedness in a fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities and logistic source

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Abstract

This paper deals with the fully parabolic attraction-repulsion chemotaxis system with signal-dependent sensitivities and logistic source, {ut=Δu−∇⋅(uχ(v)∇v)+∇⋅(uξ(w)∇w)+μu(1−u),x∈Ω,t>0,vt=Δv−v+u,x∈Ω,t>0,wt=Δw−w+u,x∈Ω,t>0 under homogeneous Neumann boundary conditions and initial conditions, where Ω⊂Rn (n≥2) is a bounded domain with smooth boundary, χ,ξ are functions satisfying some conditions and μ>0 is a constant. When χ,ξ are constants, it is known that the above system possesses a globally bounded classical solution in some cases. However, there has been no work in the case that χ,ξ are functions. This paper develops global existence and boundedness of classical solutions to the above system in such case.

Original languageEnglish
Article number124153
JournalJournal of Mathematical Analysis and Applications
Volume489
Issue number1
DOIs
Publication statusPublished - 1 Sep 2020

Keywords

  • Attraction-repulsion
  • Boundedness
  • Chemotaxis
  • Global existence

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