Details
| Original language | English |
|---|---|
| Pages (from-to) | 1499-1527 |
| Number of pages | 29 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 20 |
| Issue number | 5 |
| Publication status | Published - Jul 2015 |
| Externally published | Yes |
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.
Keywords
- Blow-up, Chemotaxis, Hyperbolic-elliptic system, Logistic source
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Applied Mathematics
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In: Discrete and Continuous Dynamical Systems - Series B, Vol. 20, No. 5, 07.2015, p. 1499-1527.
Research output: Contribution to journal › Article › Research › 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 -