Logarithmic diffusion and porous media equations: a unified description

Details Logarithmic diffusion and porous media equations: a unified description Logarithmic diffusion and porous media equations: a unified description

2005-08-14

arxiv.org/abs/cond-mat/0508343v1

Phys. Rev. E 72, 031106 (2005)

Physics

Condensed Matter

Statistical Mechanics

5 pages. To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.72.031106

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 L\'evy 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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