Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 254-279 |
| Seitenumfang | 26 |
| Fachzeitschrift | Journal of differential equations |
| Jahrgang | 271 |
| Frühes Online-Datum | 17 Sept. 2020 |
| Publikationsstatus | Veröffentlicht - 15 Jan. 2021 |
| Extern publiziert | Ja |
Abstract
Global existence and boundedness of classical solutions of the chemotaxis–consumption system nt=Δn−∇⋅(n∇c),0=Δc−nc, under no-flux boundary conditions for n and Robin-type boundary conditions ∂νc=(γ−c)g for c (with γ>0 and C1+β(∂Ω)∋g>0 for some β∈(0,1)) are established in bounded domains Ω⊂RN, N≥1. Under a smallness condition on γ, moreover, we show convergence to the stationary solution.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Journal of differential equations, Jahrgang 271, 15.01.2021, S. 254-279.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Long-term behaviour in a parabolic–elliptic chemotaxis–consumption model
AU - Fuest, Mario
AU - Lankeit, Johannes
AU - Mizukami, Masaaki
N1 - Funding Information: The first author is partially supported by the German Academic Scholarship Foundation and by the Deutsche Forschungsgemeinschaft within the project Emergence of structures and advantages in cross-diffusion systems, project number 411007140 . Publisher Copyright: © 2020 Elsevier Inc.
PY - 2021/1/15
Y1 - 2021/1/15
N2 - Global existence and boundedness of classical solutions of the chemotaxis–consumption system nt=Δn−∇⋅(n∇c),0=Δc−nc, under no-flux boundary conditions for n and Robin-type boundary conditions ∂νc=(γ−c)g for c (with γ>0 and C1+β(∂Ω)∋g>0 for some β∈(0,1)) are established in bounded domains Ω⊂RN, N≥1. Under a smallness condition on γ, moreover, we show convergence to the stationary solution.
AB - Global existence and boundedness of classical solutions of the chemotaxis–consumption system nt=Δn−∇⋅(n∇c),0=Δc−nc, under no-flux boundary conditions for n and Robin-type boundary conditions ∂νc=(γ−c)g for c (with γ>0 and C1+β(∂Ω)∋g>0 for some β∈(0,1)) are established in bounded domains Ω⊂RN, N≥1. Under a smallness condition on γ, moreover, we show convergence to the stationary solution.
KW - Boundedness
KW - Chemotaxis
KW - Chemotaxis–consumption
KW - Global existence
KW - Large-time behaviour
KW - Realistic oxygen boundary conditions
UR - http://www.scopus.com/inward/record.url?scp=85091068327&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2020.08.021
DO - 10.1016/j.jde.2020.08.021
M3 - Article
AN - SCOPUS:85091068327
VL - 271
SP - 254
EP - 279
JO - Journal of differential equations
JF - Journal of differential equations
SN - 0022-0396
ER -