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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

  • Received: 06 March 2019 Accepted: 17 July 2019 Published: 22 October 2019
  • We consider the density field $ f(x) $ generated by a volume source $ \mu(y) $ in $ D $ which is a domain in $ \mathbb{R}^3 $. For two disjoint segments $ \gamma, \Gamma_1 $ on a straight line in $ \mathbb{R}^3 \setminus \overline{D} $, we establish a conditional stability estimate of Hölder type in determining $ f $ on $ \Gamma_1 $ by data $ f $ on $ \gamma $. 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.

    Citation: Yu Chen, Jin Cheng, Giuseppe Floridia, Youichiro Wada, Masahiro Yamamoto. Conditional stability for an inverse source problem and an application to the estimation of air dose rate of radioactive substances by drone data[J]. Mathematics in Engineering, 2020, 2(1): 26-33. doi: 10.3934/mine.2020002

    Related Papers:

  • We consider the density field $ f(x) $ generated by a volume source $ \mu(y) $ in $ D $ which is a domain in $ \mathbb{R}^3 $. For two disjoint segments $ \gamma, \Gamma_1 $ on a straight line in $ \mathbb{R}^3 \setminus \overline{D} $, we establish a conditional stability estimate of Hölder type in determining $ f $ on $ \Gamma_1 $ by data $ f $ on $ \gamma $. 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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    [8] Malins A, Okumura M, Machida M, et al. Fields of view for environmental radioactivity. Proceedings of the 2015 International Symposium on Radiological Issues for Fukushima's Revitalized Future, arxiv.org/abs/1509.09125.
    [9] Saito K, Petoussi-Henss N, Zankl M (1998) Calculation of the effective dose from environmental gamma ray sources and its variation. Health Phys 74: 698-706.
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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 License (http://creativecommons.org/licenses/by/4.0)
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