Abstract
The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to asymmetric Levy flights. Our approach consists of replacing the Laplacian diffusion operator by a fractional diffusion operator of order , whose fundamental solutions are Levy -stable distributions that exhibit power law decay, . Numerical simulations of the fractional Fisher-Kolmogorov equation and analytical arguments show that anomalous diffusion leads to the exponential acceleration of the front and a universal power law decay, , of the front’s tail.
- Received 17 December 2002
DOI:https://doi.org/10.1103/PhysRevLett.91.018302
©2003 American Physical Society