Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy (Articolo in rivista)

Type
Label
  • Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy (Articolo in rivista) (literal)
Anno
  • 2009-01-01T00:00:00+01:00 (literal)
Alternative label
  • A.M. SCARFONE; T. WADA (2009)
    Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy
    in Brazilian journal of physics (Impr.)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • A.M. SCARFONE; T. WADA (literal)
Pagina inizio
  • 475 (literal)
Pagina fine
  • 482 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 39 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 2a (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Istituto Nazionale per la Fisica della Materia (CNR-INFM) and Dipartimento di Fisica, Politecnico di Torino, I-10129, Italy?; Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan. (literal)
Titolo
  • Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy (literal)
Abstract
  • 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. (literal)
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