Multidimensional advection and fractional dispersion
- 1 May 1999
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 59 (5) , 5026-5028
- https://doi.org/10.1103/physreve.59.5026
Abstract
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.Keywords
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