On pulse solutions of a reaction–diffusion system in population dynamics

Vitaly Volpert (1, 2) , Natalia Reinberg (3) , Mohammed Benmir (4) , Soumaya Boujena (4)

1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
2 MMCS - Modélisation mathématique, calcul scientifique
3 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
4 Department of Mathematics [Casablanca]

A reaction–diffusion system of equations describing the distribution of population density is considered. The existence of pulse solutions is proved by the Leray–Schauder method based on the topological degree for elliptic operators in unbounded domains and on a priori estimates of solutions. Numerical simulations show that such solutions become stable in the case of global consumption of resources while they are unstable without the integral terms. This model is used to describe human height distribution.

Domaines: Equations aux dérivées partielles [math.AP]

Vitaly Volpert, Natalia Reinberg, Mohammed Benmir, Soumaya Boujena. On pulse solutions of a reaction–diffusion system in population dynamics. Nonlinear Analysis: Theory, Methods and Applications, 2015, ⟨10.1016/j.na.2015.02.017⟩. ⟨hal-01237675⟩