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arXiv · 1906.12014

Inverse moving source problem for fractional diffusion(-wave) equations: Determination of orbits

Guanghui Hu·Yikan Liu·Masahiro Yamamoto
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Abstract

This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. 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.

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Guanghui Hu, Yikan Liu, Masahiro Yamamoto. 2019-06-28. Inverse moving source problem for fractional diffusion(-wave) equations: Determination of orbits. https://doi.org/10.1007/978-981-15-1592-7_5

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