Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.
Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.
复制标题
DOI：
10.1103/physreve.65.041108
复制
发表时间：
2002-02
期刊：
影响因子：
--
通讯作者：
I. T. Pedron;R. S. Mendes;L. Malacarne;E. Lenzi
中科院分区：
文献类型：
--
作者：
I. T. Pedron;R. S. Mendes;L. Malacarne;E. Lenzi
在这项工作中，我们纳入，在一个统一的方式，两个异常的行为，幂律和拉伸指数的，通过考虑径向依赖的N维非线性扩散方程偏微分ρ/偏微分t=nabla。（Knablarho（nu））-nabla.其中K=Dr（-theta），nu、theta、mu和D是真实的参数，F是外力，α是随时间变化的源。该方程统一了分形上的O 'Shaughnessy-Procaccia反常扩散方程（nu=1）和多孔介质中的球形反常扩散方程（theta=0）。得到了这个非线性Fokker-Planck方程的精确球对称解，从而得到了一大类反常行为。通过引入一个有效势，讨论了这类Fokker-Planck方程的定态解.
In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.