A differential equation with state-dependent delay from cell population biology
A differential equation with state-dependent delay from cell population biology
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DOI：
10.1016/j.jde.2015.12.038
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
P. Getto;M. Waurick
中科院分区：
文献类型：
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作者：
P. Getto;M. Waurick
我们分析了一个描述干细胞种群成熟的微分方程式，它具有状态相关的延迟，这是通过常微分方程组的解隐式定义的。我们详细阐述了模型成分的光滑性条件，特别是生命率，它保证了局部半流的存在，并允许指定线性变分方程。这些证明是基于Hartung等人的理论结果。与无限维中的隐式函数参数相结合。此外，我们还给出了状态依赖时滞微分方程解整体存在的判据。为了证明这一结果，我们将Hale和Lunel的一个定理应用于C_1-拓扑，并使用了Diekmann等人关于度量空间的结果。
We analyze a differential equation, describing the maturation of a stem cell population, with a state-dependent delay, which is implicitly defined via the solution of an ODE. We elaborate smoothness conditions for the model ingredients, in particular vital rates, that guarantee the existence of a local semiflow and allow to specify the linear variational equation. The proofs are based on theoretical results of Hartung et al. combined with implicit function arguments in infinite dimensions. Moreover we elaborate a criterion for global existence for differential equations with state-dependent delay. To prove the result we adapt a theorem by Hale and Lunel to the C 1-topology and use a result on metric spaces from Diekmann et al.