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 Sibirsk. Mat. Zh., 2012, Volume 53, Number 2, Pages 377–387 (Mi smj2312)

Solvability of the initial-boundary value problem for an integrodifferential equation

I. V. Prokhorov

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok

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.

Keywords: nonstationary equation, generalized matching conditions, strongly continuous semigroup.

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English version:
Siberian Mathematical Journal, 2012, 53:2, 301–309

Bibliographic databases:

UDC: 517.958

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

Citation in format AMSBIB
\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://www.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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000303357900012} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84860374030} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. V. Prokhorov, “The Cauchy problem for the radiative transfer equation with generalized conjugation conditions”, Comput. Math. Math. Phys., 53:5 (2013), 588–600
2. 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
3. I. Prokhorov, A. Sushchenko, V. Kan, E. Kovalenko, “Simulation of sonar signal propagation in a fluctuating ocean”, Proceedings of the 2015 ICU International Congress on Ultrasonics, Physics Procedia, 70, ed. N. Declercq, Elsevier Science BV, 2015, 690–694
4. 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
5. 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
6. 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
7. I. V. Prokhorov, A. A. Suschenko, “Zadacha Koshi dlya uravneniya perenosa izlucheniya v neogranichennoi srede”, Dalnevost. matem. zhurn., 18:1 (2018), 101–111
8. 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
9. Amosov A., “Nonstationary Radiation Transfer Through a Multilayered Medium With Reflection and Refraction Conditions”, Math. Meth. Appl. Sci., 41:17 (2018), 8115–8135
10. Yarovenko I.P. Prokhorov I.V., “Determination of Refractive Indices of a Layered Medium Under Pulsed Irradiation”, Opt. Spectrosc., 124:4 (2018), 567–574
11. I. V. Prokhorov, “The Cauchy Problem for the Radiation Transfer Equation with Fresnel and Lambert Matching Conditions”, Math. Notes, 105:1 (2019), 80–90
12. 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
13. I. V. Prokhorov, I. P. Yarovenko, “Zadacha Koshi dlya nestatsionarnogo uravneniya perenosa izlucheniya s komptonovskim rasseyaniem”, Sib. elektron. matem. izv., 17 (2020), 1943–1952
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