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

Solutions of Some Nonlinear Diffusion Equations and Generalized Entropy Framework

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Received: 1 August 2013; in revised form: 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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.

AMA Style

Lenzi EK, dos Santos MAF, Michels FS, Mendes RS, Evangelista LR. Solutions of Some Nonlinear Diffusion Equations and Generalized Entropy Framework. Entropy. 2013; 15(9):3931-3940.

Chicago/Turabian Style

Lenzi, Ervin K.; dos Santos, Maike A.F.; Michels, Flavio S.; Mendes, Renio S.; Evangelista, Luiz R. 2013. "Solutions of Some Nonlinear Diffusion Equations and Generalized Entropy Framework." Entropy 15, no. 9: 3931-3940.


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