Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

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

Viglialoro, Giuseppe and Woolley, Thomas E. 2019. Solvability of a Keller-Segel system with signal-dependent sensitivity and essentially sublinear production. Applicable Analysis 10.1080/00036811.2019.1569227
Item availability restricted.

[img] PDF - Accepted Post-Print Version
Restricted to Repository staff only until 21 January 2020 due to copyright restrictions.

Download (840kB)

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: In Press
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: 03 Sep 2019 10:16
URI: http://orca.cf.ac.uk/id/eprint/118269

Actions (repository staff only)

Edit Item Edit Item

Downloads

Downloads per month over past year

View more statistics