Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 4778-4806 |
Seitenumfang | 29 |
Fachzeitschrift | Journal of differential equations |
Jahrgang | 267 |
Ausgabenummer | 8 |
Publikationsstatus | Veröffentlicht - Okt. 2019 |
Extern publiziert | Ja |
Abstract
We consider the chemotaxis model {u t=Δu−∇⋅(u∇v),v t=Δv−vw,w t=−δw+u in smooth, bounded domains Ω⊂R n, n∈N, where δ>0 is a given parameter. If either n≤2 or ‖v 0‖ L ∞(Ω) ≤ [Formula presented] we show the existence of a unique global classical solution (u,v,w) and convergence of (u(⋅,t),v(⋅,t),w(⋅,t)) towards a spatially constant equilibrium, as t→∞. The proof of global existence for the case n≤2 relies on a bootstrap procedure. As a starting point we derive a functional inequality for a functional being sublinear in u, which appears to be novel in this context.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Journal of differential equations, Jahrgang 267, Nr. 8, 10.2019, S. 4778-4806.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Analysis of a chemotaxis model with indirect signal absorption
AU - Fuest, Mario
PY - 2019/10
Y1 - 2019/10
N2 - We consider the chemotaxis model {u t=Δu−∇⋅(u∇v),v t=Δv−vw,w t=−δw+u in smooth, bounded domains Ω⊂R n, n∈N, where δ>0 is a given parameter. If either n≤2 or ‖v 0‖ L ∞(Ω) ≤ [Formula presented] we show the existence of a unique global classical solution (u,v,w) and convergence of (u(⋅,t),v(⋅,t),w(⋅,t)) towards a spatially constant equilibrium, as t→∞. The proof of global existence for the case n≤2 relies on a bootstrap procedure. As a starting point we derive a functional inequality for a functional being sublinear in u, which appears to be novel in this context.
AB - We consider the chemotaxis model {u t=Δu−∇⋅(u∇v),v t=Δv−vw,w t=−δw+u in smooth, bounded domains Ω⊂R n, n∈N, where δ>0 is a given parameter. If either n≤2 or ‖v 0‖ L ∞(Ω) ≤ [Formula presented] we show the existence of a unique global classical solution (u,v,w) and convergence of (u(⋅,t),v(⋅,t),w(⋅,t)) towards a spatially constant equilibrium, as t→∞. The proof of global existence for the case n≤2 relies on a bootstrap procedure. As a starting point we derive a functional inequality for a functional being sublinear in u, which appears to be novel in this context.
KW - Chemotaxis
KW - Global existence
KW - Indirect consumption
KW - Large-time behavior
UR - http://www.scopus.com/inward/record.url?scp=85065408831&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2019.05.015
DO - 10.1016/j.jde.2019.05.015
M3 - Article
VL - 267
SP - 4778
EP - 4806
JO - Journal of differential equations
JF - Journal of differential equations
SN - 0022-0396
IS - 8
ER -