Solutions of Some Nonlinear Diffusion Equations and Generalized Entropy Framework

Entropy

Ervin K. Lenzi¹  Maike A. F. dos Santos¹  Flavio S. Michels¹  Renio S. Mendes¹ 

[1] Departamento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, Maringá-PR 87020-900, Brazil

关键词: diffusion;    Tsallis entropy;    Lévy distribution;   

DOI  :  10.3390/e15093931

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.