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This article is cited in 5 scientific papers (total in 5 papers)
Mathematical physics
Determination of the attenuation coefficient for the nonstationary radiative transfer equation
I. V. Prokhorovab, I. P. Yarovenkoa a Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia
b Far Eastern Federal University, 690950, Vladivostok, Russia
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.
Key words:
nonstationary radiative transfer equation, radiation sources, inverse problems, attenuation coefficient, tomography.
Received: 28.03.2020 Revised: 28.06.2021 Accepted: 04.08.2021
Citation:
I. V. Prokhorov, I. P. Yarovenko, “Determination of the attenuation coefficient for the nonstationary radiative transfer equation”, Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021), 2095–2108; Comput. Math. Math. Phys., 61:12 (2021), 2088–2101
Linking options:
https://www.mathnet.ru/eng/zvmmf11334 https://www.mathnet.ru/eng/zvmmf/v61/i12/p2095
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