On the stability of homogeneous steady states of a chemotaxis system with logistic growth term
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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.
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
Applied Mathematics Letters
© 2016, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.sciencedirect.com / https://dx.doi.org/10.1016/j.aml.2015.12.001
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