Criterion of positivity for semilinear problems with applications in biology

Michel Duprez (1) , Antoine Perasso (2)

1 I2M - Institut de Mathématiques de Marseille
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; Dynamic Systems; Well-Posedness; 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. Positivity, 2017, 21 (4), p. 1383-1392. ⟨10.1007/s11117-017-0474-0⟩. ⟨hal-01290966v2⟩