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

AbstractThe 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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