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 nonstandard bistable approximation of the monostable problem---and upper barriers. As a consequence, we prove the convergence to a propagating interface.
Matthieu Alfaro. Arnaud Ducrot. "Propagating interface in a monostable reaction-diffusion equation with time delay." Differential Integral Equations 27 (1/2) 81 - 104, January/February 2014. https://doi.org/10.57262/die/1384282855