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

T. Wada; A. M. Scarfone

doi:10.1140/epjb/e2009-00159-6

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arXiv · 0902.4775

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

T. Wada·A. M. Scarfone

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Abstract

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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T. Wada, A. M. Scarfone. 2009-02-27. Asymptotic solutions of a nonlinear diffusive equation in the framework of $\kappa$-generalized statistical mechanics. https://doi.org/10.1140/epjb/e2009-00159-6

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