Solutions of some nonlinear diffusion equations and generalized entropy framework

Abstract

We investigate solutions of a generalized diffusion equation that contains nonlinear terms in the presence of external forces and reaction terms. The solutions found here can have a compact or long tail behavior and can be expressed interms of the q-exponential functions present in the Tsallis framework. In the case of the long-tailed behavior, in the asymptotic limit, these solutions can also be connected with the Lévy distributions. In addition, from the results presented here, a rich class of diffusive processes, including normal and anomalous ones, can be obtained. © 2013 by the authors.