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Conditional stability for an inverse source problem and an application to the estimation of air dose rate of radioactive substances by drone data

1 School of Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, China
2 School of Mathematical Sciences, Fudan University, Shanghai, 200433, China
3 Department of Mathematics and Applications, R. Caccioppoli, University of Naples Federico II, 80126 Naples, Italy
4 Isotope Science Center, The University of Tokyo, Tokyo, 113-0032, Japan
5 Department of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153, Japan
6 Honorary Member of Academy of Romanian Scientists, Splaiul Independentei Street, no 54, 050094 Bucharest Romania

This contribution is part of the Special Issue: Inverse problems in imaging and engineering science
Guest Editors: Lauri Oksanen; Mikko Salo
Link: https://www.aimspress.com/newsinfo/1270.html

Special Issues: Inverse problems in imaging and engineering science

We consider the density field f(x) generated by a volume source μ(y) in D which is a domain in R3. For two disjoint segments γ, Γ1 on a straight line in R3 \ D, we establish a conditional stability estimate of Hölder type in determining f on Γ1 by data f on γ. This is a theoretical background for real-use solutions for the determination of air dose rates of radioactive substance at the human height level by high-altitude data. The proof of the stability estimate is based on the harmonic extension and the stability for line unique continuation of a harmonic function.
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© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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