Boundedness in a quasilinear two-species chemotaxis system with consumption of chemoattractant

This paper deals with a two-species chemotaxis system ut = ∇ · (D1(u)∇u) − ∇ · (uχ1(w)∇w) + µ1u(1 − u − a1v), x ∈ Ω, t > 0, vt = ∇ · (D2(v)∇v) − ∇ · (vχ2(w)∇w) + µ2v(1 − a2u − v), x ∈ Ω, t > 0, wt = ∆w − (αu + βv)w, x ∈ Ω, t > 0, where Ω ⊂ Rn (n ≥ 1) is a bounded domain with smooth boundary...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerzők: Zhang Jing
Hu Xuegang
Wang Liangchen
Qu Li
Dokumentumtípus: Folyóirat
Megjelent: 2019
Sorozat:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Matematikai modell, Differenciálegyenlet
doi:10.14232/ejqtde.2019.1.31

Online Access:http://acta.bibl.u-szeged.hu/62109
Leíró adatok
Tartalmi kivonat:This paper deals with a two-species chemotaxis system ut = ∇ · (D1(u)∇u) − ∇ · (uχ1(w)∇w) + µ1u(1 − u − a1v), x ∈ Ω, t > 0, vt = ∇ · (D2(v)∇v) − ∇ · (vχ2(w)∇w) + µ2v(1 − a2u − v), x ∈ Ω, t > 0, wt = ∆w − (αu + βv)w, x ∈ Ω, t > 0, where Ω ⊂ Rn (n ≥ 1) is a bounded domain with smooth boundary ∂Ω; χi(i = 1, 2) are chemotactic functions satisfying χ 0 i ≥ 0; the parameters µ1, µ2 > 0, a1, a2 > 0 and α, β > 0, the initial data (u0, v0) ∈ (C 0 (Ω))2 and w0 ∈ W1,∞(Ω) are non-negative. Based on the maximal Sobolev regularity, it is shown that this system possesses a unique global bounded classical solution provided that the logistic growth coefficients µ1 and µ2 are sufficiently large.
Terjedelem/Fizikai jellemzők:1-12
ISSN:1417-3875