Nonuniform reaction rate distribution for the generalized Fisher equation: ignition ahead of the reaction front.

We have addressed the problem of wavefront propagation for the generalized Fisher equation involving diffusion transport with a finite velocity and a spatially nonuniform reaction rate. We have considered in detail the phenomenon of wavefront jump or ignition ahead of the reaction front for a piecewise constant reaction rate. By using a relativistic mechanics technique based on the principle of least action we have found the criterion under which the ignition phenomenon happens and the time of appearance of the new front ahead of the initial reaction front.