On the stability of homogeneous steady states of a chemotaxis system with logistic growth term
On the stability of homogeneous steady states of a chemotaxis system with logistic growth term
复制标题
DOI：
10.1016/j.aml.2015.12.001
复制
发表时间：
2016-07
期刊：
影响因子：
--
通讯作者：
Mark A. J. Chaplain;J. Tello
中科院分区：
文献类型：
--
作者：
Mark A. J. Chaplain;J. Tello
考虑一类具有趋化项的抛物型-椭圆型非线性偏微分方程组。该系统模拟了在有界域Ω中群体n朝向更高浓度的化学物质c的移动。我们考虑常趋化敏感度χ和一个椭圆型方程来描述化学物质n t−d nΔn=−χdiv(n∇c)+μn(1−n)，−d cΔc+c=h(N)对于单调递增和Lipschitz函数h的分布.我们在2χ|h‘|<；μ的假设下研究了解的渐近行为.作为渐近稳定性的结果，我们得到了严格正平衡态的唯一性。
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 chemical n t− d n Δ n=− χ div (n∇ c)+ μ n (1− n),− d c Δ c+ c= h (n) for a monotone increasing and Lipschitz function h. We study the asymptotic behavior of solutions under the assumption of 2 χ| h′|< μ. As a result of the asymptotic stability we obtain the uniqueness of the strictly positive steady states.