On the stability of homogeneous steady states of a chemotaxis system with logistic growth term
Abstract
We consider a nonlinear PDEs system of Parabolic-Elliptic type with chemotactic terms. The system models the movement of a population “n” towards a higher concentration of a chemical “c” in a bounded domain Ω. We consider constant chemotactic sensitivity χ and an elliptic equation to describe the distribution of the chemicalnt − dnΔn = −χdiv(n∇c) + μn(1−n), −dcΔc + c = h(n) for a monotone increasing and lipschitz function h. We study the asymptotic behavior of solutions under the assumption of 2χ∣h′∣ < μ. As a result of the asymptotic stability we obtain the uniqueness of the strictly positive steady states.
Citation
Chaplain , M A J & Tello , J I 2016 , ' On the stability of homogeneous steady states of a chemotaxis system with logistic growth term ' , Applied Mathematics Letters , vol. 57 , pp. 1-6 . https://doi.org/10.1016/j.aml.2015.12.001
Publication
Applied Mathematics Letters
Status
Peer reviewed
ISSN
0893-9659Type
Journal article
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.