Existence of Pulses for the System of Competition of Species

Martine Marion (1, 2) , Vitaly Volpert (3, 4, 2)

1 ECL - École Centrale de Lyon
2 MMCS - Modélisation mathématique, calcul scientifique
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
4 ICJ - Institut Camille Jordan

The paper is concerned with the existence of pulses for monotone reaction-diffusion systems of two equations. For a general class of systems we prove that pulses exist if and only if the wave solutions propagate at positive speed. This result is applied to investigate the existence of pulses for the system of competition of species.

Mots clés: Existence of pulses; Monotone systems; Leray-Schauder method

Domaines: Equations aux dérivées partielles [math.AP]

Martine Marion, Vitaly Volpert. Existence of Pulses for the System of Competition of Species. Journal of Dynamics and Differential Equations, 2019, 31, pp.1653-1670. ⟨10.1007/s10884-017-9582-6⟩. ⟨hal-01573773⟩