Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1499-1527 |
| Seitenumfang | 29 |
| Fachzeitschrift | Discrete and Continuous Dynamical Systems - Series B |
| Jahrgang | 20 |
| Ausgabenummer | 5 |
| Publikationsstatus | Veröffentlicht - Juli 2015 |
| Extern publiziert | Ja |
Abstract
We define and (for q > n) prove uniqueness and an extensibility property of W '-solutions to ut = -∇ · (u ∇v) +?u - μu2 0 = Δv - v + u ∂vv|∂Ω = ∂vu|∂Ω = 0, u(0, ·) = u0, in balls in ℝn. They exist globally in time for μ ≥ 1 and, for a certain class of initial data, undergo finite-time blow-up if μ < 1. We then use this blow-up result to obtain a criterion guaranteeing some kind of structure formation in a corresponding chemotaxis system - thereby extending recent results of Winkler [26] to the higher dimensional (radially symmetric) case.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
- Mathematik (insg.)
- Angewandte Mathematik
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in: Discrete and Continuous Dynamical Systems - Series B, Jahrgang 20, Nr. 5, 07.2015, S. 1499-1527.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Chemotaxis can prevent thresholds on population density
AU - Lankeit, Johannes
PY - 2015/7
Y1 - 2015/7
N2 - We define and (for q > n) prove uniqueness and an extensibility property of W '-solutions to ut = -∇ · (u ∇v) +?u - μu2 0 = Δv - v + u ∂vv|∂Ω = ∂vu|∂Ω = 0, u(0, ·) = u0, in balls in ℝn. They exist globally in time for μ ≥ 1 and, for a certain class of initial data, undergo finite-time blow-up if μ < 1. We then use this blow-up result to obtain a criterion guaranteeing some kind of structure formation in a corresponding chemotaxis system - thereby extending recent results of Winkler [26] to the higher dimensional (radially symmetric) case.
AB - We define and (for q > n) prove uniqueness and an extensibility property of W '-solutions to ut = -∇ · (u ∇v) +?u - μu2 0 = Δv - v + u ∂vv|∂Ω = ∂vu|∂Ω = 0, u(0, ·) = u0, in balls in ℝn. They exist globally in time for μ ≥ 1 and, for a certain class of initial data, undergo finite-time blow-up if μ < 1. We then use this blow-up result to obtain a criterion guaranteeing some kind of structure formation in a corresponding chemotaxis system - thereby extending recent results of Winkler [26] to the higher dimensional (radially symmetric) case.
KW - Blow-up
KW - Chemotaxis
KW - Hyperbolic-elliptic system
KW - Logistic source
UR - http://www.scopus.com/inward/record.url?scp=84941802057&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1403.1837
DO - 10.48550/arXiv.1403.1837
M3 - Article
AN - SCOPUS:84941802057
VL - 20
SP - 1499
EP - 1527
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 5
ER -