On the stability of homogeneous steady states of a chemotaxis system with logistic growth term

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• 作者：M.A.J. Chaplain^a ; J.I. Tello^b ; ^{j.tello@upm.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Chemotaxis ; Stability ; Steady state ; Lower and upper solutions
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：57
• 期：Complete
• 页码：1-6
• 全文大小：542 K

文摘

We consider a nonlinear PDEs system of Parabolic–Elliptic type with chemotactic terms. The system models the movement of a population “n$n$” towards a higher concentration of a chemical “c$c$” in a bounded domain Ω$\Omega$.

We consider constant chemotactic sensitivity χ$\chi$ and an elliptic equation to describe the distribution of the chemical

for a monotone increasing and Lipschitz function h$h$.

We study the asymptotic behavior of solutions under the assumption of 2χ|h^′|<μ$2\chi \left|h^{\prime }\right|<\mu$. As a result of the asymptotic stability we obtain the uniqueness of the strictly positive steady states.