The Age-Structured Chemostat with Substrate Dynamics as a Control System
Iasson Karafyllis, Dionysis Theodosis and Miroslav Krstic
在这项工作中,我们研究了一个具有更新边界条件和耦合基板方程的年龄结构的切度模型。 该模型是非线性的,由双曲偏微分方程和普通微分方程组成,其中非线性,非局部项出现在普通微分方程和边界条件中。 两个微分方程都包含一个非负控制输入,而模型的状态要求为正。 在适当的弱解决方案框架下,我们确定该模型的状态空间和输入空间。 我们为所有可接受的初始条件和所有允许的控制输入证明了全球存在和解决方案的独特性。 为此,我们采用了巴拿赫的定点定理与隐式求解公式和有用的求值估计的组合。 最后,我们表明,年龄结构的切度模型在度量空间上给出了一个定义良好的控制系统。
In this work we study an age-structured chemostat model with a renewal boundary condition and a coupled substrate equation. The model is nonlinear and consists of a hyperbolic partial differential equation and an ordinary differential equation with nonlinear, nonlocal terms appearing both in the ordinary differential equation and the boundary condition. Both differential equations contain a non-negative control input, while the states of the model are required to be positive. Under an appropriat...