Existence and asymptotics of traveling wave fronts for a coupled nonlocal diffusion and difference system with delay - Abdennasser Chekroun (Electronic Journal of Qualitative Theory of Differential Equations, 2019)
In this paper, we consider a general study of a recent proposed hematopoietic stem cells model. This model is a combination of nonlocal diffusion equation and difference equation with delay. We deal with the properties of traveling waves for this system such as the existence and asymptotic behavior. By using the Schauder's fixed point theorem combined with the method based on the construction of upper and lower solutions, we obtain the existence of traveling wave fronts for a speed $c> c^{\star}$. The case $c= c^{\star}$ is studied by using a limit argument. We prove also that $c^{\star}$ is the critical value. We finally prove that the nonlocality increases the minimal wave speed.