Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 16
135
Views
0
CrossRef citations to date
0
Altmetric
Articles

Boundedness in a two-species chemotaxis-consumption system with nonlinear diffusion and sensitivity

ORCID Icon &
Pages 3530-3545 | Received 27 Nov 2019, Accepted 20 Jan 2020, Published online: 03 Feb 2020
 

ABSTRACT

This paper deals with the following two-species chemotaxis system ut=(D1(u)u)(S1(u)w)+μ1u(1ua1v),xΩ, t>0,vt=(D2(v)v)(S2(v)w)+μ2v(1a2uv),xΩ, t>0,wt=Δw(u+v)w,xΩ, t>0 with homogeneous Neumann boundary conditions and suitable initial conditions, where ΩRn (n1) is a bounded and smooth domain. Moreover, the parameters μ1,μ2>0, and a1,a2>0. For i = 1, 2, we assume that Di(s)cDi(s+1)mi1andSi(s)cSi(s+1)qi1withSi(s)0foralls0, where cDi>0, cSi>0, miR and qiR. Then if one of the following cases holds:

  1. qi<mi2+2nn+2;

  2. qi<mi2+32 and μi is sufficiently large,

it is proved that the system possesses a unique global bounded classical solution.

MSC (2010) Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

X. Hu is supported by Natural Science Foundation of Chongqing [grant No. cstc2017jcyjBX0037].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.