title: 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 superdiffusion like a Lévy kind. In addition an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension, is obtained. This unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes.
authors.affiliation: Universidade Estadual do Oeste do Paraná, Rua Pernambuco, 1777, 85960-000, Marechal Cândido Rondon, Paraná, Brazil.
authors.forename: I T
authors.initials: IT
authors.lastname: Pedron
authors.forename: R S
authors.initials: RS
authors.lastname: Mendes
authors.forename: T J
authors.initials: TJ
authors.lastname: Buratta
authors.forename: L C
authors.initials: LC
authors.lastname: Malacarne
authors.forename: E K
authors.initials: EK
authors.lastname: Lenzi