Nonlinear equation for anomalous diffusion: Unified power-law and stretched exponential exact solution - art. no. 030101

摘要

The nonlinear diffusion equation partial derivative rho/partial derivativet=D<()over tilde>rho (nu) is analyzed here, where <()over tilde>=(1/r(d-1))(partial derivative/partial derivativer)r(d-1-theta)partial derivative/partial derivativer, 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-)d]. Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy. [References: 19]