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Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements

Author

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  • Sergey Pyatkov

    (Institute of Digital Economics, Yugra State University, Chekhov St. 16, 628007 Khanty-Mansiysk, Russia
    Academy of Sciences of the Republic of Sakha (Yakutia), 33 Lenin Ave., 677007 Yakutsk, Russia)

  • Denis Shilenkov

    (Institute of Digital Economics, Yugra State University, Chekhov St. 16, 628007 Khanty-Mansiysk, Russia)

Abstract

Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed. They are smoothness conditions on the data, geometric conditions on the location of measurement points, and the boundary of a domain. The proof relies on asymptotics of fundamental solutions to the corresponding elliptic problems and the Laplace transform. The inverse problem is reduced to a linear algebraic system with a nondegerate matrix.

Suggested Citation

  • Sergey Pyatkov & Denis Shilenkov, 2022. "Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements," Mathematics, MDPI, vol. 10(9), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1549-:d:808587
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    References listed on IDEAS

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    1. Shoubin Wang & Li Zhang & Xiaogang Sun & Huangchao Jia, 2017. "Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-9, July.
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