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

Philipp Getto, Marcus Waurick

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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 C1-topology and use a result on metric spaces from Diekmann et al.

Original languageEnglish
Pages (from-to)6176-6200
JournalJournal of Differential Equations
Volume260
Issue number7
Early online date6 Jan 2016
DOIs
Publication statusPublished - 5 Apr 2016

Keywords

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

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