Multidimensional advection and fractional dispersion.
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.
Meerschaert
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Department of Mathematics (084), University of Nevada, Reno, Nevada 89557, USA. mcubed@unr.edu
Benson
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Bäumer
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