The existence and non-existence of traveling waves of scalar reaction-diffusion-advection equation in unbounded cylinder

This paper is concerned with the existence and non-existence of traveling wave solutions of reaction-diffusion-advection equation with boundary conditions of mixed type in unbounded cylinder. By constructing new supper-sub solutions and applying monotone iteration method, we obtain existence of traveling wave solutions with wave velocity bigger than the “minimal speed”. For wave velocity smaller than the “minimal speed”, we find that traveling waves of exponential decay do not exist. Finally, we apply our results to KPP type nonlinearity.