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Boundedness in a parabolic-elliptic chemotaxis system with nonlinear diffusion and sensitivity, and logistic source

Viglialoro, Giuseppe and Woolley, Thomas 2018. Boundedness in a parabolic-elliptic chemotaxis system with nonlinear diffusion and sensitivity, and logistic source. Mathematical Methods in the Applied Sciences 41 (5) , pp. 1809-1824. 10.1002/mma.4707
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Abstract

In this paper, we study the zero flux chemotaxis system where Ω is a bounded and smooth domain of urn:x-wiley:mma:media:mma4707:mma4707-math-0002, n≥1, and where urn:x-wiley:mma:media:mma4707:mma4707-math-0003, k,μ>0 and α≤1. For any v≥0, the chemotactic sensitivity function is assumed to behave as the prototype χ(v)=χ0/(1+av)2, with a≥0 and χ0>0. We prove that for any nonnegative and sufficiently regular initial data u(x,0), the corresponding initial‐boundary value problem admits a unique global bounded classical solution if α<1; indeed, for α=1, the same conclusion is obtained provided μ is large enough. Finally, we illustrate the range of dynamics present within the chemotaxis system in 1, 2, and 3 dimensions by means of numerical simulations.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Wiley: 12 months
ISSN: 0170-4214
Date of First Compliant Deposit: 19 December 2017
Date of Acceptance: 24 November 2017
Last Modified: 26 Jul 2018 06:46
URI: http://orca.cf.ac.uk/id/eprint/107584

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