Superfast front propagation in reactive systems with non-Gaussian diffusion

Abstract

We study a reaction diffusion system where we consider a non-gaussian process\ninstead of a standard diffusion. If the process increments follow a probability\ndistribution with tails approaching to zero faster than a power law, the usual\nqualitative behaviours of the standard reaction diffusion system, i.e.,\nexponential tails for the reacting field and a constant front speed, are\nrecovered. On the contrary if the process has power law tails, also the\nreacting field shows power law tail and the front speed increases exponentially\nwith time. The comparison with other reaction-transport systems which exhibit\nanomalous diffusion shows that, not only the presence of anomalous diffusion,\nbut also the detailed mechanism, is relevant for the front propagation.\n