生理结构种群的模拟：更新方程和偏微分方程
Modelling physiologically structured populations: renewal equations and partial differential equations
摘要：
我们分析了一类线性更新方程的测度值解的长期行为生理结构人口建模。更新方程，我们认为其特征在于由一个正则化性质的内核。这种正则化属性允许推导出大的时间行为的测量值的解决方案的渐近行为的绝对连续的，相对于勒贝格测度，组件。我们将结果应用于细胞生长和裂变的模型以及免疫力减弱和增强的模型。对于这两个模型，我们与更新方程（RE）的偏微分方程（PDE）制定和得出结论的偏微分方程的解决方案的渐近行为。
英文摘要：
We analyse the long term behaviour of the measure-valued solutions of a class of linear renewal equations modelling physiologically structured populations. The renewal equations that we consider are characterised by a regularisation property of the kernel. This regularisation property allows to deduce the large time behaviour of the measure-valued solutions from the asymptotic behaviour of their absolutely continuous, with respect to the Lebesgue measure, component. We apply the results to a model of cell growth and fission and to a model of waning and boosting of immunity. For both models we relate the renewal equation (RE) to the partial differential equation (PDE) formulation and draw conclusions about the asymptotic behaviour of the solutions of the PDEs.
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