pp 1–10 | Cite as

Criterion of positivity for semilinear problems with applications in biology



The goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical biology: epidemiology, predator-prey interactions and oncology.


Positivity Well-posedness Dynamic systems Semilinear problems Population dynamics 

Mathematics Subject Classification

35A01 35B09 35Q92 92D25 


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© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Institut de Mathmatiques de Marseille UMR CNRS 7373Université Aix-MarseilleMarseille Cedex 13France
  2. 2.Chrono-environnement UMR CNRS 6249Université Bourgogne Franche-ComtéBesançonFrance

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