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

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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.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku Tokyo, 153-8914, Japan

    Yikan Liu

  2. Department of Mathematics, Texas A & M University, College Station, TX, 77843-3368, USA

    William Rundell

  3. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Masahiro Yamamoto

Authors
  1. Yikan Liu
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  2. William Rundell
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  3. Masahiro Yamamoto
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Correspondence to Yikan Liu.

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Liu, Y., Rundell, W. & Yamamoto, M. Strong maximum principle for fractional diffusion equations and an application to an inverse source problem. FCAA 19, 888–906 (2016). https://doi.org/10.1515/fca-2016-0048

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  • DOI: https://doi.org/10.1515/fca-2016-0048

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