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

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

2009-02-27

arxiv.org/abs/0902.4775v1

Physics

Condensed Matter

Statistical Mechanics

Submitted to EPJB

Scientific paper

The asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the $\kappa$-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the $\kappa$-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 $\kappa$-Gaussian function. Simple argument based on a time-dependent transformation performed on the related $\kappa$-generalized Fokker-Planck equation, supports this conclusion.

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