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

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.

Submitted to EPJB

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Cited by in corpus (11)

• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Maximum entropy principle and power-law tailed distributions
• k-Deformed Fourier Transform
• A nonlinear drift which leads to $\kappa$-generalized distributions
• Relativistic kinetics and power-law tailed distributions
• Relativistic Roots of $\kappa$-Entropy
• Power-Law tailed statistical distributions and Lorentz transformations
• From the Fokker-Planck equation to a contact Hamiltonian system
• Density matrix for a consistent non-extensive thermodynamics
• Maximum entropy generation in open systems: the Fourth Law?
• Irreversibility and maximum generation in $\kappa$-generalized statistical mechanics