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

Frassu S.;Viglialoro G.

2022-01-01

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Abstract

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, in Ω×(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‖Ljavax.xml.bind.JAXBElement@65b04462(Ω) obeys certain constraints, functions of n and ξ (0