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Determination of the Attenuation Coefficient for the Nonstationary Radiative Transfer Equation

Determination of the Attenuation Coefficient for the Nonstationary Radiative Transfer Equation For the nonstationary radiative transfer equation, the inverse problem of determining the attenuation coefficient from a known solution at the domain boundary is considered. The structure and the continuous properties of the solution to an initial-boundary value problem for the radiative transfer equation are studied. Under special assumptions about the radiation source, it is shown that the inverse problem has a unique solution and a formula for the Radon transform of the attenuation coefficient is derived. The quality of the reconstructed tomographic images of the sought function is analyzed numerically in the case of various angular and time flux density distributions of the external source. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Mathematics and Mathematical Physics Springer Journals

Determination of the Attenuation Coefficient for the Nonstationary Radiative Transfer Equation

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References (44)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2021. ISSN 0965-5425, Computational Mathematics and Mathematical Physics, 2021, Vol. 61, No. 12, pp. 2088–2101. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2021, Vol. 61, No. 12, pp. 2095–2108.
ISSN
0965-5425
eISSN
1555-6662
DOI
10.1134/s0965542521120101
Publisher site
See Article on Publisher Site

Abstract

For the nonstationary radiative transfer equation, the inverse problem of determining the attenuation coefficient from a known solution at the domain boundary is considered. The structure and the continuous properties of the solution to an initial-boundary value problem for the radiative transfer equation are studied. Under special assumptions about the radiation source, it is shown that the inverse problem has a unique solution and a formula for the Radon transform of the attenuation coefficient is derived. The quality of the reconstructed tomographic images of the sought function is analyzed numerically in the case of various angular and time flux density distributions of the external source.

Journal

Computational Mathematics and Mathematical PhysicsSpringer Journals

Published: Dec 1, 2021

Keywords: nonstationary radiative transfer equation; radiation sources; inverse problems; attenuation coefficient; tomography

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