Logarithmic diffusion and porous media equations: a unified description
Statistical Mechanics
2016-08-31 v1
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 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.
Cite
@article{arxiv.cond-mat/0508343,
title = {Logarithmic diffusion and porous media equations: a unified description},
author = {I. T. Pedron and R. S. Mendes and T. J. Buratta and L. C. Malacarne and E. K. Lenzi},
journal= {arXiv preprint arXiv:cond-mat/0508343},
year = {2016}
}
Comments
5 pages. To appear in Phys. Rev. E