Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution

Details Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution

2000-10-10

arxiv.org/abs/cond-mat/0010142v1

Phys. Rev. E63 (2001) 030101(R).

Physics

Condensed Matter

Statistical Mechanics

3 pages, 2 eps figures

Scientific paper

10.1103/PhysRevE.63.030101

The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, 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 ($\theta=0$). 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.

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