Solvability of a Keller-Segel system with signal-dependent sensitivity and essentially sublinear production

Viglialoro, Giuseppe and Woolley, Thomas E. ORCID: https://orcid.org/0000-0001-6225-5365 2020. Solvability of a Keller-Segel system with signal-dependent sensitivity and essentially sublinear production. Applicable Analysis 99 (14) , pp. 2507-2525. 10.1080/00036811.2019.1569227

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Abstract

In this paper, we consider the zero-flux chemotaxis system ut0=Δu−∇⋅(uχ(v)∇v) in Ω×(0,∞),=Δv−v+g(u) in Ω×(0,∞), in a smooth and bounded domain Ω of R2. The chemotactic sensitivity χ is a general nonnegative function from C1((0,∞)) while g, the production of the chemical signal v, belongs to C1([0,∞)) and satisfies λ1≤g(s)≤λ2(1+s)β, for all s≥ 0, 0≤β<1 and 0<λ1≤λ2. It is established that no chemotactic collapse for the cell distribution u occurs in the sense that any arbitrary nonnegative and sufficiently regular initial data u(x,0) emanates a unique pair of global and uniformly bounded functions (u,v) which classically solve the corresponding initial boundary value problem. Finally, we illustrate the range of dynamics present within the chemotaxis system by means of numerical simulations.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Taylor & Francis
ISSN:	0003-6811
Date of First Compliant Deposit:	10 January 2019
Date of Acceptance:	4 January 2019
Last Modified:	07 Nov 2023 04:22
URI:	https://orca.cardiff.ac.uk/id/eprint/118269

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