Boundedness for the chemotaxis system in a flux limitation with indirect signal production

A fully parabolic chemotaxis system with indirect signal production{ut=Δu−∇⋅(uf(|∇v|2)∇v),x∈Ω,t>0,vt=Δv−v+w,x∈Ω,t>0,wt=Δw−w+u,x∈Ω,t>0 is considered in a smooth bounded domain Ω⊂Rn (n≥1) under homogeneous Neumann boundary conditions, where the flux limitation f∈C2([0,∞)) is given suitably re...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 538; no. 1; p. 128364
Main Authors Lv, Huilin, Zheng, Shenzhou
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2024
Subjects
Chemotaxis system
Flux limitation
Global boundedness
Indirect signal
Flux limitation
Chemotaxis system
Indirect signal
Global boundedness
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Summary:A fully parabolic chemotaxis system with indirect signal production{ut=Δu−∇⋅(uf(|∇v|2)∇v),x∈Ω,t>0,vt=Δv−v+w,x∈Ω,t>0,wt=Δw−w+u,x∈Ω,t>0 is considered in a smooth bounded domain Ω⊂Rn (n≥1) under homogeneous Neumann boundary conditions, where the flux limitation f∈C2([0,∞)) is given suitably regular satisfyingf(ξ)≤Kf(1+ξ)−αforallξ≥0 with some Kf>0 and α∈R. The range of α depending on the dimension n ensures the existence of a global bounded classical solution for the associated initial-boundary value problem, in which sense any collapse is excluded.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128364