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

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.

arXiv comment15 pages

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• Inverse $t$-source problem and a strict positivity property for coupled subdiffusion systems
• Numerical schemes for reconstructing profiles of moving sources in (time-fractional) evolution equations