Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source
Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source
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DOI：
10.3934/dcdsb.2017094
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发表时间：
2017-03
影响因子：
1.2
通讯作者：
Ke Lin;Chunlai Mu
中科院分区：
文献类型：
--
作者：
Ke Lin;Chunlai Mu
本文考虑高维光滑有界区域上的三个抛物型方程组\开始{document}$\left\{\开始{array}{llll}u_t=\Delta u-\chi_1\nabla\cdot（u\nabla w）+\mu_1u（1-u-a_1v），\quad x '>描述了两个种群之间的相互竞争.对于任意交叉扩散系数$\chi_1>0$和$\chi_2>0$以及速率$a_1>0$和$a_2>0$，证明了当参数$\mu_1$和$\mu_2$足够大时，对于足够正则的初始数据，整体经典有界解存在.在推导该方程组解的收敛性时，我们需要区分两种情况：a_1，a_2\in[0，1）$和a_1>1$以及a_2
In this paper, we consider a system of three parabolic equations in high-dimensional smoothly bounded domain \begin{document}$\left\{\begin{array}{llll}u_t=\Delta u-\chi_1\nabla\cdot( u\nabla w)+\mu_1u(1-u-a_1v),\quad x'>which describes the mutual competition between two populations on account of the Lotka-Volterra dynamics. For any cross-diffusivities $\chi_1>0$ and $\chi_2>0$ and the rates $a_1>0$ and $a_2>0$, it is proved that the global classical bounded solutions exist for sufficiently regular initial data when the parameters $\mu_1$ and $\mu_2$ are sufficiently large. In deriving the convergence of solutions to this system, we need to distinguish two cases $a_1, a_2\in[0, 1)$ and $a_1>1$ and $0\leq a_2