Abstract:
Under study is the well-posedness of the Cauchy problem for the nonstationary radiation transfer equation with generalized matching conditions at the interface between the media. We prove the existence of a unique strongly continuous semigroup of resolvents, estimate its order of growth, and consider the question of stabilization of the nonstationary solution.
Citation:
I. V. Prokhorov, “Solvability of the initial-boundary value problem for an integrodifferential equation”, Sibirsk. Mat. Zh., 53:2 (2012), 377–387; Siberian Math. J., 53:2 (2012), 301–309
\Bibitem{Pro12}
\by I.~V.~Prokhorov
\paper Solvability of the initial-boundary value problem for an integrodifferential equation
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 2
\pages 377--387
\mathnet{http://mi.mathnet.ru/smj2312}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2975942}
\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 2
\pages 301--309
\crossref{https://doi.org/10.1134/S0037446612020127}
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Linking options:
https://www.mathnet.ru/eng/smj2312
https://www.mathnet.ru/eng/smj/v53/i2/p377
This publication is cited in the following 23 articles:
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V A Kan, A A Sushchenko, E R Lyu, I A Baranchugov, “Investigation of the Seabed Profile taking into account the Multiple Scattering Approximation of Radiation”, IOP Conf. Ser.: Earth Environ. Sci., 988:3 (2022), 032059
I. V. Prokhorov, I. P. Yarovenko, “Zadacha Koshi dlya nestatsionarnogo uravneniya perenosa izlucheniya s komptonovskim rasseyaniem”, Sib. elektron. matem. izv., 17 (2020), 1943–1952
I. V. Prokhorov, “The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions”, Math. Notes, 105:1 (2019), 80–90
A. Kim, I. V. Prokhorov, “Initial-boundary value problem for a radiative transfer equation with generalized matching conditions”, Sib. elektron. matem. izv., 16 (2019), 1036–1056
A A Sushchenko, E R Lyu, V A Kan, “Methods of the Theory of Radiation Transfer for Bathymetry Problems”, IOP Conf. Ser.: Earth Environ. Sci., 272:2 (2019), 022140
A A Sushchenko, P A Vornovskikh, V A Kan, “Algorithms of Determination of the Boundaries Shaded Seabottom Areas”, IOP Conf. Ser.: Earth Environ. Sci., 272:2 (2019), 022242
I. V. Prokhorov, A. A. Suschenko, “Zadacha Koshi dlya uravneniya perenosa izlucheniya v neogranichennoi srede”, Dalnevost. matem. zhurn., 18:1 (2018), 101–111
A. Kim, I. V. Prokhorov, “Theoretical and numerical analysis of an initial-boundary value problem for the radiative transfer equation with Fresnel matching conditions”, Comput. Math. Math. Phys., 58:5 (2018), 735–749
Amosov A., “Nonstationary Radiation Transfer Through a Multilayered Medium With Reflection and Refraction Conditions”, Math. Meth. Appl. Sci., 41:17 (2018), 8115–8135
Yarovenko I.P. Prokhorov I.V., “Determination of Refractive Indices of a Layered Medium Under Pulsed Irradiation”, Opt. Spectrosc., 124:4 (2018), 567–574
A. A. Amosov, “Initial-Boundary Value Problem for the Non-Stationary Radiative Transfer Equation with Fresnel Reflection and Refraction Conditions”, J Math Sci, 231:3 (2018), 279
I. V. Prokhorov, A. A. Sushchenko, A. Kim, “An initial boundary value problem for the radiative transfer equation with diffusion matching conditions”, J. Appl. Industr. Math., 11:1 (2017), 115–124
Olga N. Trofimova, Kseniya A. Kuruntyaeva, Andrey E. Kovtanyuk, Igor V. Prokhorov, 2017 Days on Diffraction (DD), 2017, 319
Andrey Sushchenko, Polina Vornovskikh, Oleg A. Romanovskii, 23rd International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, 2017, 257
A. Kim, I. V. Prokhorov, 2017 Days on Diffraction (DD), 2017, 168
A. Kim, I. V. Prokhorov, “Monte Carlo method for non-stationary radiative transfer equation in inhomogeneous media”, 22nd International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, Proceedings of SPIE, 10035, eds. G. Matvienko, O. Romanovskii, SPIE-Int. Soc. Optical Engineering, 2016, 100350Z
A. Amosov, M. Shumarov, “Boundary value problem for radiation transfer equation in multilayered medium with reflection and refraction conditions”, Appl. Anal., 95:7, SI (2016), 1581–1597
A. A. Amosov, “Radiative Transfer Equation with Fresnel Reflection and Refraction Conditions in a System of Bodies with Piecewise Smooth Boundaries”, J Math Sci, 219:6 (2016), 821
I. V. Prokhorov, A. A. Sushchenko, “On the well-posedness of the Cauchy problem for the equation of radiative transfer with Fresnel matching conditions”, Siberian Math. J., 56:4 (2015), 736–745
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