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We consider a monostable time-delayed reaction-diffusion equation arisingfrom population dynamics models. We let a small parameter tend to zero andinvestigate 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 propagatinginterface.

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