论文标题
建模生理结构化种群：更新方程和部分微分方程
Modelling physiologically structured populations: renewal equations and partial differential equations
论文作者
论文摘要
我们分析了一类线性更新方程对生理结构化种群建模的线性更新方程的长期行为。我们认为的续签方程的特征是内核的正则化属性。这种正则化属性允许从其绝对连续的渐近行为（相对于Lebesgue度量组成部分）推断出测量值的大量时间行为。我们将结果应用于细胞生长和裂变模型，以及免疫力减弱和增强的模型。对于这两个模型，我们将续签方程（RE）与部分微分方程（PDE）配方联系起来，并得出有关PDE溶液渐近行为的结论。
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.
