具有PDE型间接信号消耗的趋化系统解的全局存在性与一致有界性

Global Existence and Uniform Boundedness of the Solution ofChemotaxis System with PDE-type Indirect Signal Consumption

本文研究了全抛物系统u t=Δu-▽·(u▽v)v t=Δv-vw w t=Δw-δw+u,其中Ω∈n,n≤3是一个具有光滑边界Ω的有界区域,参数δ>0。近年来,学者们对生物趋化性的研究越来越多,与间接信号产生的趋化模型相比,间接信号消耗的趋化模型得到的结果较少。本文的目的是研究在齐次Neumann边界条件下具有PDE型间接信号消耗的趋化系统解的全局存在性与一致有界性。结果表明,当空间维数n≤3时,对于任意非负且适当的初始数据,相应的初边值问题具有唯一的全局经典解,且该解是一致有界的。

This paper talks about the fully parabolic system u t=Δu-▽·(u▽v)v t=Δv-vw w t==Δw-δw+u,whereΩ∈n,n≤3 is a bounded region with smooth boundaryΩand parameterδ>0.In recent years,scholars has conducted more and more studies on biological chemotaxis.However,few results are concluded on chemotaxis model with indirect signal consumption when compared to that of chemotaxis model with indirect signal production.The purpose of this paper is to study the global existence and uniform boundedness of the solution of chemoattractant system with PDE type indirect signal consumption under homogeneous Neumann boundary conditions.The results show that the corresponding initial-boundary value problem for any nonnegative and suitably regular initial data possesses a unique and uniformly bounded global classical solution if the space dimension n≤3.