title: Nonlinear equation for anomalous diffusion: Unified power-law and stretched exponential exact solution.
abstract: The nonlinear diffusion equation partial delta rho/delta t=D Delta rho(nu) is analyzed here, where Delta[triple bond](1/r(d-1))(delta/delta r)r(d-1-theta) delta/delta r, and d, theta, and nu are real parameters. This equation unifies the anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact point-source solution is obtained, enabling us to describe a large class of subdiffusion [ theta>(1-nu)d], "normal" diffusion [theta=(1-nu)d] and superdiffusion [theta<(1-nu)d]. Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy.
authors: Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900, Maringá-PR, Brazil.
authors: L C
authors: LC
authors: Malacarne
authors: R S
authors: RS
authors: Mendes
authors: I T
authors: IT
authors: Pedron
authors: E K
authors: EK
authors: Lenzi