Diff. Geom, Math. Phys., PDE Seminar: Tingting Huan

We show the nonexistence of traveling fronts in the combustion model with fractional Laplacian (-\Delta)^s when s\in(0,1/2]. Our method can be used to give a direct and simple proof of the nonexistence of traveling fronts for the usual Fisher-KPP nonlinearity. Also we prove the existence and nonexistence of traveling waves solutions for different ranges of the fractional power s for the generalized Fisher-KPP type model.