The Riesz-Bessel fractional diffusion equation.

Anh, V. V. and Mcvinish, R. (2004) The Riesz-Bessel fractional diffusion equation.. Applied Mathematics and Optimization, 49 3: 241-264. doi:10.1007/s00245-004-0790-1


Author Anh, V. V.
Mcvinish, R.
Title The Riesz-Bessel fractional diffusion equation.
Journal name Applied Mathematics and Optimization   Check publisher's open access policy
ISSN 0095-4616
Publication date 2004-05-01
Sub-type Article (original research)
DOI 10.1007/s00245-004-0790-1
Volume 49
Issue 3
Start page 241
End page 264
Total pages 24
Place of publication New York
Publisher Springer
Language eng
Subject 010404 Probability Theory
Abstract This paper examines the properties of a fractional diffusion equation defined by the composition of the inverses of the Riesz potential and the Bessel potential. The first part determines the conditions under which the Green function of this equation is the transition probability density function of a Lévy motion. This Lévy motion is obtained by the subordination of Brownian motion, and the Lévy representation of the subordinator is determined. The second part studies the semigroup formed by the Green function of the fractional diffusion equation. Applications of these results to certain evolution equations is considered. Some results on the numerical solution of the fractional diffusion equation are also provided. [ABSTRACT FROM AUTHOR] Copyright of Applied Mathematics & Optimization is the property of Springer Science & Business Media B.V. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts)
Keyword Anomalous diffusion
Fractional diffusion equation
Lévy motion
Stochastic evolution equation
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mathematics and Physics
 
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Created: Wed, 04 Feb 2009, 18:52:57 EST by Judy Dingwall on behalf of Mathematics