An exactly solvable model of subdiffusion-reaction front propagation

The propagation of a reaction front is considered in the framework of the Seki-Lindenberg reaction-subdiffusion model, which is appropriate in the case of a diffusion-limited reaction. Typically, this kind of problem is solved using approximate approaches or numerical methods. We apply a model piecewise linear reaction function, which allows for exact analytical solutions. For a front between two stable homogeneous states, a unique value of the front velocity is found. In the case of fronts between a stable and an unstable state, a family of traveling wave solutions is revealed. The conditions for the existence of a special 'pushed' front are considered. The influence of advection on the front velocity is also analyzed.