Analysis of fronts in reaction-dispersal processes.

The existence of traveling wave front solutions with a minimum speed selected for reaction-dispersal processes is studied. We obtain a general existence condition in terms of the waiting time and dispersal distance probability distribution functions and we detail this result for situations of ecological interest. In particular, when particles disperse according to jumps of short length and any waiting time probability distribution function, we show that the minimum speed selection for traveling wave fronts is not always possible, so the waiting time and the dispersal distance distributions cannot be arbitrarily chosen.