A differential equation with state-dependent delay from cell population biology

作者：Getto Philipp^*; Waurick Marcus

来源：Journal of Differential Equations, 2016, 260(7): 6176-6200.

DOI：10.1016/j.jde.2015.12.038

• Delay differential equation
• State-dependent delay
• Semiflow
• Global existence
• Structured populations
• Stem cell model

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.

• 出版日期2016-4-5