Boundedness in a two-species chemotaxis parabolic system with two chemicals
Boundedness in a two-species chemotaxis parabolic system with two chemicals
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DOI：
10.3934/dcdsb.2017132
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发表时间：
2017-04
影响因子：
1.2
通讯作者：
Xie Li;Yilong Wang
中科院分区：
文献类型：
--
作者：
Xie Li;Yilong Wang
本文致力于趋化系统 \begin{document}$\left\{\begin{aligned}u'>，该系统模拟了两种化学物质存在下两个物种之间的相互作用，其中 \begin{document}$χ, \, xiε\mathbb{R}$\end{document} , \begin{document}$Ω\subset\mathbb{R}^2$\end{document} 是具有平滑边界的有界域。结果表明，在齐次诺依曼边界条件下，系统具有唯一的全局经典解，只要 \begin{document}$\int_Ω u_0dx$\end{document} 和 \begin{document}$\int_Ω w_0dx$\end{document} 都适当小，该解就有界。特别是，我们将Tao和Winkler（2015，Disc.Cont.Dyn.Syst.B）最近获得的结果扩展到完全抛物线情况，即 \begin{document}$τ=1$\end{document} 的情况。
This paper is devoted to the chemotaxis system \begin{document}$\left\{\begin{aligned}u'>which models the interaction between two species in presence of two chemicals, where \begin{document}$χ, \, ξ∈\mathbb{R}$\end{document} , \begin{document}$Ω\subset\mathbb{R}^2$\end{document} are bounded domains with smooth boundary. It is shown that under the homogeneous Neumann boundary conditions the system possesses a unique global classical solution which is bounded whenever both \begin{document}$\int_Ω u_0dx$\end{document} and \begin{document}$\int_Ω w_0dx$\end{document} are appropriately small. In particular, we extend the recent results obtained by Tao and Winkler (2015, Disc. Cont. Dyn. Syst. B) to the fully parabolic case, i.e., the case of \begin{document}$τ=1$\end{document} .