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Fractional Calculus and Applied Analysis

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Strong maximum principle for fractional diffusion equations and an application to an inverse source problem

Yikan Liu / William Rundell / Masahiro Yamamoto
Published Online: 2016-08-31 | DOI: https://doi.org/10.1515/fca-2016-0048

Abstract

The strong maximum principle is a remarkable property of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corresponding weak maximum principle, in this paper we establish a strong maximum principle for time-fractional diffusion equations with Caputo derivatives, which is slightly weaker than that for the parabolic case. As a direct application, we give a uniqueness result for a related inverse source problem on the determination of the temporal component of the inhomogeneous term.

MSC 2010: Primary 35R11; Secondary 26A33; 35B50; 35R30

Key Words and Phrases: fractional diffusion equation; Caputo derivative; strong maximum principle; Mittag-Leffler function; inverse source problem; fractional Duhamel's principle

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About the article

Published Online: 2016-08-31

Published in Print: 2016-08-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 19, Issue 4, Pages 888–906, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2016-0048.

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