Propagating interface in a monostable reaction-diffusion equation with time delay

Matthieu Alfaro (1) , Arnaud Ducrot (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 IMB - Institut de Mathématiques de Bordeaux

We consider a monostable time-delayed reaction-diffusion equation arising from population dynamics models. We let a small parameter tend to zero and investigate the behavior of the solutions. We construct accurate lower barriers --- by using a non standard bistable approximation of the monostable problem--- and upper barriers. As a consequence, we prove the convergence to a propagating interface.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Alfaro, Arnaud Ducrot. Propagating interface in a monostable reaction-diffusion equation with time delay. Differential and integral equations, 2014, 27 (1-2), pp.81-104. ⟨hal-00735081⟩