Propagation failure for a front between stable states in a system with subdiffusion

The propagation of subdiffusion-reaction fronts is studied in the framework of a model recently suggested by Fedotov [Phys. Rev. E 81, 011117 (2010)PLEEE81539-375510.1103/PhysRevE.81.011117]. An exactly solvable model with a piecewise linear reaction function is considered. A drastic difference between the cases of normal diffusion and subdiffusion has been revealed. While in the case of normal diffusion, a traveling wave solution between two locally stable phases always exists, and is unique, in the case of the subdiffusion such solutions do not exist. The numerical simulation shows that the velocity of the front decreases with time according to a power law. The only kind of fronts moving with a constant velocity are waves which propagate solely due to the reaction, with a vanishing subdiffusive flux.