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.
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Wada, T., Scarfone, A. Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics. Eur. Phys. J. B 70, 65–71 (2009). https://doi.org/10.1140/epjb/e2009-00159-6
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DOI: https://doi.org/10.1140/epjb/e2009-00159-6