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

This article is cited in 13 scientific papers (total in 13 papers)

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.

Full text: PDF file (305 kB)
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English version:
Siberian Mathematical Journal, 2012, 53:2, 301–309

Bibliographic databases:

UDC: 517.958
Received: 16.05.2011

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
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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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    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  crossref  isi  scopus
    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  crossref  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
    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  mathnet  crossref  crossref  mathscinet  elib
    7. I. V. Prokhorov, A. A. Suschenko, “Zadacha Koshi dlya uravneniya perenosa izlucheniya v neogranichennoi srede”, Dalnevost. matem. zhurn., 18:1 (2018), 101–111  mathnet
    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  mathnet  crossref  crossref  isi  elib
    9. Amosov A., “Nonstationary Radiation Transfer Through a Multilayered Medium With Reflection and Refraction Conditions”, Math. Meth. Appl. Sci., 41:17 (2018), 8115–8135  crossref  mathscinet  zmath  isi
    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  crossref  isi  scopus
    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  mathnet  crossref  crossref  mathscinet  isi  elib
    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  mathnet  crossref
    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  mathnet  crossref
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