Logarithmic diffusion and porous media equations: a unified description

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.

5 pages. To appear in Phys. Rev. E

References in corpus (1)

• Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions

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