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Journal of Evolution Equations

, Volume 18, Issue 4, pp 1853–1888 | Cite as

A system of state-dependent delay differential equation modeling forest growth I: semiflow properties

  • Pierre Magal
  • Zhengyang Zhang
Article
  • 15 Downloads

Abstract

In this article, we investigate the semiflow properties of a class of state-dependent delay differential equations which is motivated by some models describing the dynamics of the number of adult trees in forests. We investigate the existence and uniqueness of a semiflow in the space of Lipschitz and \(C^1\) weighted functions. We obtain a blow-up result when the time approaches the maximal time of existence. We conclude the paper with an application of a spatially structured forest model.

Keywords

State-dependent delay differential equations Forest population dynamics Semiflow Time of blow-up 

Mathematics Subject Classification

34K05 37L99 37N25 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.UMR 5251, IMBUniversity of BordeauxBordeauxFrance
  2. 2.UMR 5251, CNRSIMBTalenceFrance

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