Criterion of positivity for semilinear problems with applications in biology

Michel Duprez (1) , Antoine Perasso (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 LCE - Laboratoire Chrono-environnement (UMR 6249)

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.

Mots clés: Positivity; Well-Posedness; Dynamic Systems; Semilinear Problems; Population Dynamics

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Santé publique et épidémiologie

Michel Duprez, Antoine Perasso. Criterion of positivity for semilinear problems with applications in biology. 2016. ⟨hal-01290966v1⟩