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Regularity and Unique Existence of Solution to Linear Diffusion Equation with Multiple Time-Fractional Derivatives

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Control and Optimization with PDE Constraints

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 164))

Abstract

We consider an initial/boundary value problem for linear diffusion equation with multiple fractional time derivatives and prove the regularity of the solution. The regularity argument implies the unique existence of the solution.

The first named author thanks JASSO Honors Scholarship and the Global COE Program “The Research and Training Center for New Development in Mathematics” at Graduate School of Mathematical Sciences of The University of Tokyo for financial support.

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Acknowledgements

The authors thank Mr. Zhiyuan Li (The University of Tokyo) for his careful reading and remarks, and the anonymous referees for valuable comments which are useful for improving the manuscript.

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Authors and Affiliations

  1. Faculty of Mathematics, Lothar Collatz School for Computing in Science, Universität Hamburg, Gindelberg 5, 20144, Hamburg, Germany

    Susanne Beckers

  2. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-9 Komaba Meguro, Tokyo, 153-8914, Japan

    Masahiro Yamamoto

Authors
  1. Susanne Beckers
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  2. Masahiro Yamamoto
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Corresponding author

Correspondence to Masahiro Yamamoto .

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Editors and Affiliations

  1. , Institute for Mathematics and Scientific, University of Graz, Heinrichstr. 36, Graz, 8010, Austria

    Kristian Bredies

  2. , Institute for Mathematics and Scientific, University of Graz, Heinrichstr. 36, Graz, 8010, Austria

    Christian Clason

  3. , Institute for Mathematics and Scientific, University of Graz, Heinrichstr. 36, Graz, 8010, Austria

    Karl Kunisch  & Gregory von Winckel  & 

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Beckers, S., Yamamoto, M. (2013). Regularity and Unique Existence of Solution to Linear Diffusion Equation with Multiple Time-Fractional Derivatives. In: Bredies, K., Clason, C., Kunisch, K., von Winckel, G. (eds) Control and Optimization with PDE Constraints. International Series of Numerical Mathematics, vol 164. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0631-2_3

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