no. 1
Partial differential equations
Boundedness in a full parabolic two-species chemotaxis system
[Les solutions d'un système de chimiotaxie à deux espèces, complètement parabolique, sont bornées]

Présenté par : the Editorial Board

Htwe, Myo Win1 ; Wang, Yifu1
1 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China
Comptes Rendus. Mathématique, Tome 355 (2017) no. 1, pp. 80-83.

Cette Note étudie les systèmes de chimiotaxie à deux espèces du type

{ut=△u−∇⋅(uχ1(w)∇w)+μ1u(1−u−a1v),x∈Ω,t>0,vt=△v−∇⋅(vχ2(w)∇w)+μ2v(1−a2u−v),x∈Ω,t>0,wt=dΔw−w+u+v,x∈Ω,t>0
où Ω est un domaine borné de Rn avec n≥1, d>0, μi≥0, i=1,2, sont des paramètres et χi, i=1,2, sont des fonctions satisfaisant certaines conditions. Notre propos est de montrer que, sous des conditions plus faibles que celles faites jusqu'à présent dans la littérature, les solutions d'un tel système sont globalement bornées.

This paper is concerned with the two-species chemotaxis system

{ut=△u−∇⋅(uχ1(w)∇w)+μ1u(1−u−a1v),x∈Ω,t>0,vt=△v−∇⋅(vχ2(w)∇w)+μ2v(1−a2u−v),x∈Ω,t>0,wt=dΔw−w+u+v,x∈Ω,t>0
in a bounded smooth domain Ω⊂Rn(n≥1), where d>0,μi≥0 and ai≥0 (i=1,2) are parameters, χi are functions satisfying some conditions. The purpose of this paper is to show the global boundedness of solutions to the above system under weaker conditions than those assumed in the related literature.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.10.024
Htwe, Myo Win 1 ; Wang, Yifu 1

1 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China 
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Htwe, Myo Win; Wang, Yifu. Boundedness in a full parabolic two-species chemotaxis system. Comptes Rendus. Mathématique, Tome 355 (2017) no. 1, pp. 80-83. doi : 10.1016/j.crma.2016.10.024. http://www.numdam.org/articles/10.1016/j.crma.2016.10.024/

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