Strong maximum principle for multi-term time-fractional diffusion equations and its application to an inverse source problem

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• 作者：Yikan Liu ^{ykliu@ms.u-tokyo.ac.jp}
• 关键词：Fractional diffusion equation ; Strong maximum principle ; Multinomial Mittag-Leffler function ; Inverse source problem
• 刊名：Computers & Mathematics with Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：73
• 期：1
• 页码：96-108
• 全文大小：470 K
• 卷排序：73

文摘

In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of practical importance. Exploiting the solution properties and the involved multinomial Mittag-Leffler functions, we improve the weak maximum principle for the multi-term time-fractional diffusion equation to a stronger one, which is parallel to that for its single-term counterpart as expected. As a direct application, we prove the uniqueness for determining the temporal component of the source term with the help of the fractional Duhamel’s principle for the multi-term case.