Details
| Original language | English |
|---|---|
| Article number | 21 |
| Number of pages | 20 |
| Journal | Zeitschrift fur Angewandte Mathematik und Physik |
| Volume | 76 |
| Issue number | 1 |
| Early online date | 24 Dec 2024 |
| Publication status | Published - Feb 2025 |
Abstract
This paper concerns the asymptotics of certain parabolic–elliptic chemotaxis-consumption systems with logistic growth and constant concentration of chemoattractant on the boundary. First we prove that in two dimensional bounded domains there exists a unique global classical solution which is uniformly bounded in time, and then, we show that if the concentration of chemoattractant on the boundary is sufficiently low, then the solution converges to the positive steady state as time goes to infinity.
Keywords
- Boundedness, Chemotaxis, Consumption of chemoattractant, Global existence, Local existence, Logistic growth, Long-time asymptotics, Nonzero boundary conditions
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Physics and Astronomy(all)
- General Physics and Astronomy
- Mathematics(all)
- Applied Mathematics
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In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 76, No. 1, 21, 02.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Asymptotics of a chemotaxis-consumption-growth model with nonzero Dirichlet conditions
AU - Knosalla, Piotr
AU - Lankeit, Johannes
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2025/2
Y1 - 2025/2
N2 - This paper concerns the asymptotics of certain parabolic–elliptic chemotaxis-consumption systems with logistic growth and constant concentration of chemoattractant on the boundary. First we prove that in two dimensional bounded domains there exists a unique global classical solution which is uniformly bounded in time, and then, we show that if the concentration of chemoattractant on the boundary is sufficiently low, then the solution converges to the positive steady state as time goes to infinity.
AB - This paper concerns the asymptotics of certain parabolic–elliptic chemotaxis-consumption systems with logistic growth and constant concentration of chemoattractant on the boundary. First we prove that in two dimensional bounded domains there exists a unique global classical solution which is uniformly bounded in time, and then, we show that if the concentration of chemoattractant on the boundary is sufficiently low, then the solution converges to the positive steady state as time goes to infinity.
KW - Boundedness
KW - Chemotaxis
KW - Consumption of chemoattractant
KW - Global existence
KW - Local existence
KW - Logistic growth
KW - Long-time asymptotics
KW - Nonzero boundary conditions
UR - http://www.scopus.com/inward/record.url?scp=85212969206&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2408.10080
DO - 10.48550/arXiv.2408.10080
M3 - Article
AN - SCOPUS:85212969206
VL - 76
JO - Zeitschrift fur Angewandte Mathematik und Physik
JF - Zeitschrift fur Angewandte Mathematik und Physik
SN - 0044-2275
IS - 1
M1 - 21
ER -