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The unique identification of variable-order fractional wave equations

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Abstract

We analyze the well-posedness and smoothing properties of a variable-order time-fractional wave partial differential equation in multiple space dimensions. Accordingly, we prove the unique determination of the variable order in this model with the observations of the unknown solutions on an arbitrarily small spatial domain over a sufficiently small time interval. The proved theorem provides a guidance where the measurements should be taken and ensure the unique identification of the variable order.

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Acknowledgements

The authors would like to express their most sincere thanks to the referees for their very helpful comments and suggestions, which greatly improved the quality of this paper. All data generated or analyzed during this study are included in this article.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Xiangcheng Zheng

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Hong Wang

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  1. Xiangcheng Zheng
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  2. Hong Wang
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Correspondence to Hong Wang.

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This work was partially funded by the ARO MURI Grant W911NF-15-1-0562 and by the National Science Foundation under Grant DMS-2012291.

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Zheng, X., Wang, H. The unique identification of variable-order fractional wave equations. Z. Angew. Math. Phys. 72, 100 (2021). https://doi.org/10.1007/s00033-021-01476-z

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  • DOI: https://doi.org/10.1007/s00033-021-01476-z

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