Eur. Phys. J. B 70, 65-71 (2009)
https://doi.org/10.1140/epjb/e2009-00159-6

Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics

¹ Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan
² Istituto Nazionale di Fisica della Materia (CNR-INFM) and Dipartimento di Fisica, Politecnico di Torino, 10129, Italy

Corresponding authors: ^a wada@mx.ibaraki.ac.jp - ^b antonio.scarfone@polito.it

Received: 21 November 2008
Revised: 5 February 2009
Published online: 5 May 2009

Abstract

The asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the κ-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the κ-Gaussian function is not a scale invariant solution of the generalized diffusive equation. Notwithstanding, several numerical simulations, with different initial conditions, show that the solutions asymptotically approach to the κ-Gaussian function. Simple argument based on a time-dependent transformation performed on the related κ-generalized Fokker-Planck equation, supports this conclusion.