Resumo

SCARFONE, A. M.  e  WADA, T.. Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy. Braz. J. Phys. [online]. 2009, vol.39, n.2a, pp. 475-482. ISSN 0103-9733.  http://dx.doi.org/10.1590/S0103-97332009000400024.

In the framework of the statistical mechanics based on the Sharma-Taneja-Mittal entropy we derive a family of nonlinear Fokker-Planck equations characterized by the associated non-increasing Lyapunov functional. This class of equations describes kinetic processes in anomalous mediums where both super-diffusive and subdiffusive mechanisms arise contemporarily and competitively. We classify the Lie symmetries and derive the corresponding group-invariant solutions for the physically meaningful Uhlenbeck-Ornstein process. For the purely diffusive process we show that any localized state asymptotically approaches a bell shape well fitted by a generalized Gaussian which is, in general, a quasi-self-similar solution for this class of purely diffusive equations.

Palavras-chave : Nonlinear Fokker-Planck equation; Sharma-Taneja-Mittal entropy; Lie symmetries; Group invariant solutions.