Inverse Moving Source Problem for Fractional Diffusion(-Wave) Equations: Determination of Orbits

This paper is concerned with the inverse problem on determining the orbit of a moving source in fractional diffusion(-wave) equations either in a connected bounded domain of or in the whole space Based on a newly established fractional Duhamel’s principle, we derive a Lipschitz stability estimate in the case of a localized moving source by the observation data at d interior points. The uniqueness for the general non-localized moving source is verified with additional data of more interior observations. © 2020, Springer Nature Singapore Pte Ltd.

Authors
Hu G. 1 , Liu Y. 2 , Yamamoto M. 3, 4, 5
Conference proceedings
Springer Proceedings in Mathematics and Statistics
Publisher
Springer New York LLC
Language
English
Pages
81-100
State
Published
DOI
10.1007/978-981-15-1592-7_5
Volume
310
Year
2020
Organizations
  • 1 Beijing Computational Science Research Center, Building 9, East Zone, ZPark II, No. 10 Xibeiwang East Road, Haidian District, Beijing, 100193, China
  • 2 Research Institute for Electronic Science, Hokkaido University, N12W7, Kita-Ward, Sapporo, 060-0812, Japan
  • 3 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
  • 4 Honorary Member of Academy of Romanian Scientists, Splaiul Independentei Street, No. 54, Bucharest, 050094, Romania
  • 5 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
Keywords
Fractional diffusion(-wave) equation; Fractional Duhamel’s principle; Inverse moving source problem; Lipschitz stability; Uniqueness
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