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On Time-Fractional Diffusion Equations with Space-Dependent Variable Order

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Abstract

This paper deals with mathematical problems related to space-dependent anomalous diffusion processes. Namely, we investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We establish that variable-order time-fractional Cauchy problems admit a unique weak solution and prove that the space-dependent variable-order coefficient is uniquely determined by the knowledge of a suitable time sequence of partial initial-boundary maps.

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Acknowledgements

The two first authors would like to thank the Department of Mathematical Sciences of The University of Tokyo, where part of this article was written, for its kind hospitality. All the authors are partially supported by Grants-in-Aid for Scientific Research (S) 15H05740 and (S) 26220702, Japan Society for the Promotion of Science. The publication has been prepared with the support of the “RUDN University Program 5-100.”

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Authors and Affiliations

  1. CNRS, CPT, Université de Toulon, Aix Marseille University, Marseille, France

    Yavar Kian & Eric Soccorsi

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

    Masahiro Yamamoto

  3. Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, Russian Federation, 117198

    Masahiro Yamamoto

Authors
  1. Yavar Kian
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  2. Eric Soccorsi
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  3. Masahiro Yamamoto
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Correspondence to Eric Soccorsi.

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Communicated by Claude-Alain Pillet.

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Kian, Y., Soccorsi, E. & Yamamoto, M. On Time-Fractional Diffusion Equations with Space-Dependent Variable Order. Ann. Henri Poincaré 19, 3855–3881 (2018). https://doi.org/10.1007/s00023-018-0734-y

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  • DOI: https://doi.org/10.1007/s00023-018-0734-y

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