Multidimensional advection and fractional dispersion.
Multidimensional advection and fractional dispersion.
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DOI：
10.1103/physreve.59.5026
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发表时间：
1999-05
期刊：
影响因子：
--
通讯作者：
M. Meerschaert;D. Benson;Boris Bäumer
中科院分区：
文献类型：
--
作者：
M. Meerschaert;D. Benson;Boris Bäumer
将分数阶扩散方程推广到二维或三维并不像推广二阶方程那样简单。这是由方程的解决方案：不像高斯，最一般的稳定向量不能产生一个原子的措施，在坐标轴上。单位球上最大偏斜稳定变量的随机组合生成扩散粒子的一般模型的稳定向量。子集是对称稳定向量，以前出现在文献和著名的多维布朗运动。在这个过程中定义了一个多维分数阶微分算子。
Extension of the fractional diffusion equation to two or three dimensions is not as simple as extension of the second-order equation. This is revealed by the solutions of the equations: unlike the Gaussian, the most general stable vector cannot be generated with an atomistic measure on the coordinate axes. A random combination of maximally skewed stable variables on the unit sphere generates a stable vector that is a general model of a diffusing particle. Subsets are symmetric stable vectors that have previously appeared in the literature and the well-known multidimensional Brownian motion. A multidimensional fractional differential operator is defined in the process.