Details
| Original language | English |
|---|---|
| Pages (from-to) | 2033-2062 |
| Number of pages | 30 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 29 |
| Issue number | 11 |
| Early online date | 9 Sept 2019 |
| Publication status | Published - 1 Oct 2019 |
| Externally published | Yes |
Abstract
Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been experimentally observed. Following the suggestions that the main reason for that is the usage of inappropriate boundary conditions, in this paper we study the solutions to the stationary chemotaxis system in bounded domains ω RN, N ≥ 1, under the no-flux boundary conditions for n and the physically meaningful condition vc = (γ-c)g on c, with the given parameter γ > 0 and g ϵ C1+β(ω), Β. ϵ (0, 1), satisfying g ≤ 0, g 0 on δω. We prove the existence and uniqueness of solutions for any given massn > 0. These solutions are nonconstant.
Keywords
- Chemotaxis, Signal consumption, Stationary solution
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Applied Mathematics
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In: Mathematical Models and Methods in Applied Sciences, Vol. 29, No. 11, 01.10.2019, p. 2033-2062.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stationary solutions to a chemotaxis-consumption model with realistic boundary conditions for the oxygen
AU - Braukhoff, Marcel
AU - Lankeit, Johannes
N1 - Funding Information: Marcel Braukhoff was funded by the Austrian Science Fund (FWF) Project F 65. Johannes Lankeit acknowledges support of the Deutsche Forschungsgemeinschaft within the Project Analysis of chemotactic cross-diffusion in complex frameworks.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been experimentally observed. Following the suggestions that the main reason for that is the usage of inappropriate boundary conditions, in this paper we study the solutions to the stationary chemotaxis system in bounded domains ω RN, N ≥ 1, under the no-flux boundary conditions for n and the physically meaningful condition vc = (γ-c)g on c, with the given parameter γ > 0 and g ϵ C1+β(ω), Β. ϵ (0, 1), satisfying g ≤ 0, g 0 on δω. We prove the existence and uniqueness of solutions for any given massn > 0. These solutions are nonconstant.
AB - Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been experimentally observed. Following the suggestions that the main reason for that is the usage of inappropriate boundary conditions, in this paper we study the solutions to the stationary chemotaxis system in bounded domains ω RN, N ≥ 1, under the no-flux boundary conditions for n and the physically meaningful condition vc = (γ-c)g on c, with the given parameter γ > 0 and g ϵ C1+β(ω), Β. ϵ (0, 1), satisfying g ≤ 0, g 0 on δω. We prove the existence and uniqueness of solutions for any given massn > 0. These solutions are nonconstant.
KW - Chemotaxis
KW - Signal consumption
KW - Stationary solution
UR - http://www.scopus.com/inward/record.url?scp=85072249132&partnerID=8YFLogxK
U2 - 10.1142/s0218202519500398
DO - 10.1142/s0218202519500398
M3 - Article
AN - SCOPUS:85072249132
VL - 29
SP - 2033
EP - 2062
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 11
ER -