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REGULARITY OF SOLUTIONS TO A TIME-FRACTIONAL DIFFUSION EQUATION

Part of: Partial differential equations Representations of solutions

Published online by Cambridge University Press:  18 July 2011

WILLIAM MCLEAN
WILLIAM MCLEAN*
Affiliation:
School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia (email: w.mclean@unsw.edu.au)
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Abstract

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We prove estimates for the partial derivatives of the solution to a time-fractional diffusion equation posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is typically less regular than in the familiar case of classical diffusion.

Keywords

fractional derivativeLaplace transformSobolev spacesingular behaviour

MSC classification

Secondary: 35B65: Smoothness and regularity of solutions 35C15: Integral representations of solutions 35C20: Asymptotic expansions
Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 2 , October 2010 , pp. 123 - 138
Copyright
Copyright © Australian Mathematical Society 2011

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