Non-existence of stationary pattern of a chemotaxis model with logistic growth

In this paper we study the non-existence of non-constant steady state (i.e., stationary pattern) for a Chemotaxis model with the volume-filling effect and logistic cell growth. We establish the critical value of the chemotactic coefficient between the existence and the non-existence of stationary pa...

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Bibliographic Details
Published in:Nonlinear analysis 2014-08, Vol.105, p.3-9
Main Authors: Ma, Manjun, Hu, Jiajia, Tao, Jicheng, Tong, Changqing
Format: Article
Language:English
Subjects:
Covering
Heterogeneous steady state
Logistic growth
Logistics
Mathematical analysis
Mathematical models
Maximum principle
Non-existence
Nonlinearity
Steady state
Theorems
Volume-filling chemotaxis model
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Summary:In this paper we study the non-existence of non-constant steady state (i.e., stationary pattern) for a Chemotaxis model with the volume-filling effect and logistic cell growth. We establish the critical value of the chemotactic coefficient between the existence and the non-existence of stationary pattern. The proofs mainly rely on the Maximum Principle, the Implicit Function Theorem and the Finite Covering Theorem. This work is a supplement and perfection of the known reference.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2014.03.009