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Entropy 2013, 15(9), 3931-3940; doi:10.3390/e15093931

Solutions of Some Nonlinear Diffusion Equations and Generalized Entropy Framework

Departamento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, Maringá-PR 87020-900, Brazil
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Received: 1 August 2013 / Revised: 26 August 2013 / Accepted: 11 September 2013 / Published: 18 September 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
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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 in terms 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 L´evy distributions. In addition, from the results presented here, a rich class of diffusive processes, including normal and anomalous ones, can be obtained.
Keywords: diffusion; Tsallis entropy; Lévy distribution diffusion; Tsallis entropy; Lévy distribution
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Lenzi, E.K.; dos Santos, M.A.F.; Michels, F.S.; Mendes, R.S.; Evangelista, L.R. Solutions of Some Nonlinear Diffusion Equations and Generalized Entropy Framework. Entropy 2013, 15, 3931-3940.

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