Superfast front propagation in reactive systems with anomalous diffusion

摘要

We study a reaction diffusion system where we consider a non-gaussian processinstead of a standard diffusion. If the process increments follow a probabilitydistribution with tails approaching to zero faster than a power law, the usualqualitative behaviours of the standard reaction diffusion system, i.e.,exponential tails for the reacting field and a constant front speed, arerecovered. On the contrary if the process has power law tails, also thereacting field shows power law tail and the front speed increases exponentiallywith time. The comparison with other reaction-transport systems which exhibitanomalous diffusion shows that, not only the presence of anomalous diffusion,but also the detailed mechanism, is relevant for the front propagation.