Boundedness criteria for a class of indirect (and direct) chemotaxis-consumption models in high dimensions

In a bounded and smooth domain Ω of Rn, n≥5, we, mainly, consider for some ξ,χ,δ positive and Tmax∈(0,∞] the zero-flux chemotaxis model with indirect signal absorption ut=ξΔu−χ∇⋅(u∇v),vt=Δv−wv,wt=−δw+u,inΩ×(0,Tmax),equipped with sufficiently regular initial data u(x,0)=u0(x)≥0, v(x,0)=v0(x)≥0 and w(...

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Bibliographic Details
Published in:Applied mathematics letters 2022-10, Vol.132, p.108108, Article 108108
Main Authors: Frassu, Silvia, Viglialoro, Giuseppe
Format: Article
Language:English
Subjects:
Boundedness
Chemotaxis
Global existence
Indirect consumption
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Summary:In a bounded and smooth domain Ω of Rn, n≥5, we, mainly, consider for some ξ,χ,δ positive and Tmax∈(0,∞] the zero-flux chemotaxis model with indirect signal absorption ut=ξΔu−χ∇⋅(u∇v),vt=Δv−wv,wt=−δw+u,inΩ×(0,Tmax),equipped with sufficiently regular initial data u(x,0)=u0(x)≥0, v(x,0)=v0(x)≥0 and w(x,0)=w0(x)≥0. We establish the existence of ξ∗=ξ∗(n)>1 such that whenever χ‖v0‖L∞(Ω) obeys certain constraints, functions of n and ξ (0
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2022.108108