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Logarithmic diffusion and porous media equations: a unified description

I. T. Pedron·R. S. Mendes·T. J. Buratta·L. C. Malacarne·E. K. Lenzi
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Abstract

In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a lorentzian form, consequently this equation characterizes a super diffusion like a Lévy kind. In addition is obtained an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension. This unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes.

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I. T. Pedron, R. S. Mendes, T. J. Buratta, L. C. Malacarne, E. K. Lenzi. 2005-08-14. Logarithmic diffusion and porous media equations: a unified description. https://doi.org/10.1103/physreve.72.031106

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