Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption
Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption
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DOI：
10.3934/dcds.2017262
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发表时间：
2016-08
期刊：
影响因子：
--
通讯作者：
J. Lankeit;Yulan Wang
中科院分区：
文献类型：
--
作者：
J. Lankeit;Yulan Wang
本文研究了$N$维有界光滑域上具有适当正则正初始数据的趋化消耗系统\begin{eqnarray*} \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot (u\nabla v)+\kappa u-\mu u^2,\\ v_t=\Delta v-uv, \end{array} \end{eqnarray*}的齐次Neumann边值问题。对于适当大的$\mu$，我们将建立一个整体有界经典解的存在性，并证明对于任意$\mu>0$，存在一个弱解。此外，在$\kappa>0$收敛到恒定平衡$(\frac{\kappa}{\mu},0)$的情况下，显示。
This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \begin{eqnarray*} \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot (u\nabla v)+\kappa u-\mu u^2,\\ v_t=\Delta v-uv, \end{array} \end{eqnarray*} in $N$-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large $\mu$ and prove that for any $\mu>0$ there exists a weak solution. Moreover, in the case of $\kappa>0$ convergence to the constant equilibrium $(\frac{\kappa}{\mu},0)$ is shown.