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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Matematikai modell, Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.31 |
| Online Access: | http://acta.bibl.u-szeged.hu/62109 |
| 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. |
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| Terjedelem/Fizikai jellemzők: | 1-12 |
| ISSN: | 1417-3875 |