Details
| Original language | English |
|---|---|
| Pages (from-to) | 6099-6121 |
| Number of pages | 23 |
| Journal | Discrete and Continuous Dynamical Systems- Series A |
| Volume | 37 |
| Issue number | 12 |
| Publication status | Published - 2017 |
Abstract
This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system (Equation presented)in N-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large μ and prove that for any μ > 0 there exists a weak solution. Moreover, in the case of κ > 0 convergence to the constant equilibrium (κ/μ, 0) is shown.
Keywords
- Asymptotic stability, Boundedness, Chemotaxis, Global existence, Logistic source, Weak solution
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Discrete and Continuous Dynamical Systems- Series A, Vol. 37, No. 12, 2017, p. 6099-6121.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption
AU - Lankeit, J.
AU - Wang, Yulan
N1 - Funding Information: gemeinschaft within the project Analysis of chemotactic cross-diffusion in complex frameworks. Y. Wang was supported by the NNSF of China (no. 11501457). Funding Information: J. Lankeit acknowledges support of the Deutsche Forschungsgemeinschaft within the project Analysis of chemotactic cross-diffusion in complex frameworks. Y. Wang was supported by the NNSF of China (no. 11501457). ∗ Corresponding author: Johannes Lankeit.
PY - 2017
Y1 - 2017
N2 - This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system (Equation presented)in N-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large μ and prove that for any μ > 0 there exists a weak solution. Moreover, in the case of κ > 0 convergence to the constant equilibrium (κ/μ, 0) is shown.
AB - This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system (Equation presented)in N-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large μ and prove that for any μ > 0 there exists a weak solution. Moreover, in the case of κ > 0 convergence to the constant equilibrium (κ/μ, 0) is shown.
KW - Asymptotic stability
KW - Boundedness
KW - Chemotaxis
KW - Global existence
KW - Logistic source
KW - Weak solution
UR - http://www.scopus.com/inward/record.url?scp=85028864614&partnerID=8YFLogxK
U2 - 10.3934/dcds.2017262
DO - 10.3934/dcds.2017262
M3 - Article
VL - 37
SP - 6099
EP - 6121
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
SN - 1078-0947
IS - 12
ER -