Geodesic
An initial boundary value problem for the radiative transfer equation with diffusion matching conditions
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 75-85.

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We consider the Cauchy problem for the nonstationary equation of radiative transfer with generalized matching conditions describing the diffusion reflection and refraction on the separation boundary of the media. We prove solvability of the initial boundary value problem and obtainh stabilization conditions for an unsteady solution.
Keywords: diffusion matching conditions, integro-differential equation, nonstationary equation, Cauchy problem, Hille–Yosida theorem. 
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I. V. Prokhorov; A. A. Sushchenko; A. Kim. An initial boundary value problem for the radiative transfer equation with diffusion matching conditions. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 75-85. http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a7/

[1] Cherchinyani K., Teoriya i prilozheniya uravneniya Boltsmana, Mir, M., 1978

[2] Isimaru A., Rasprostranenie i rasseyanie voln v sluchaino-neodnorodnykh sredakh, Mir, M., 1981

[3] Derevtsov E. Yu., “Chislennoe reshenie zadachi refraktsionnoi tomografii v tsilindricheskoi oblasti”, Sib. zhurn. industr. matematiki, 18:4 (2015), 30–41 | MR | Zbl

[4] Prokhorov I. V., Suschenko A. A., “Issledovanie zadachi akusticheskogo zondirovaniya morskogo dna metodami teorii perenosa izlucheniya”, Akusticheskii zhurn., 61:3 (2015), 400–408 | DOI

[5] Prokhorov I. V., Suschenko A. A., Kan V. A., “Ob odnoi zadache opredeleniya relefa dna fluktuiruyuschego okeana”, Sib. zhurn. industr. matematiki, 18:2 (2015), 99–110 | MR | Zbl

[6] Vladimirov V. S., “Matematicheskie zadachi odnoskorostnoi teorii perenosa chastits”, Tr. MIAN SSSR, 61, 1961, 3–158 | MR

[7] Marchuk G. I., Lebedev V. I., Chislennye metody v teorii perenosa neitronov, Atomizdat, M., 1981

[8] Novikov V. M., Shikhov S. B., Teoriya parametricheskogo vozdeistviya na perenos neitronov, Energoizdat, M., 1982

[9] Germogenova T. A., Lokalnye svoistva reshenii uravneniya perenosa, Nauka, M., 1986 | MR

[10] Anikonov D. S., Konovalova D. S., “Kineticheskoe uravnenie perenosa dlya sluchaya komptonovskogo rasseyaniya”, Sib. mat. zhurn., 43:5 (2002), 987–1001 | MR | Zbl

[11] Anikonov D. S., Konovalova D. S., “Kraevaya zadacha dlya uravneniya perenosa s chisto komptonovskim rasseyaniem”, Sib. mat. zhurn., 46:1 (2005), 3–16 | MR | Zbl

[12] Yarovenko I. P., “O razreshimosti kraevoi zadachi dlya uravneniya perenosa izlucheniya s uchetom komptonovskogo rasseyaniya”, Dalnevost. mat. zhurn., 14:1 (2014), 109–121 | MR | Zbl

[13] Anikonov D. S., Kovtanyuk A. E., Prokhorov I. V., Ispolzovanie uravneniya perenosa v tomografii, Logos, M., 2000

[14] Anikonov D. S., Nazarov V. G., Prokhorov I. V., Poorly Visible Media in X-ray Tomography, VSP, Utrecht–Boston, 2002 | Zbl

[15] Prokhorov I. V., Yarovenko I. P., “Issledovanie zadach opticheskoi tomografii metodami teorii perenosa izlucheniya”, Optika i spektroskopiya, 101:5 (2006), 817–824

[16] Prokhorov I. V., Yarovenko I. P., Nazarov V. G., “Optical tomography problems at layered media”, Inverse Problems, 24:2 (2008), Article number 025019 | DOI | MR | Zbl

[17] Prokhorov I. V., “Kraevaya zadacha teorii perenosa izlucheniya v neodnorodnoi srede s usloviyami otrazheniya na granitse”, Differents. uravneniya, 36:6 (2000), 848–851 | MR | Zbl

[18] Prokhorov I. V., “Opredelenie poverkhnosti razdela sred po dannym tomograficheskogo prosvechivaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 42:10 (2002), 1542–1555 | MR | Zbl

[19] Prokhorov I. V., “O razreshimosti kraevoi zadachi dlya uravneniya perenosa izlucheniya s obobschennymi usloviyami sopryazheniya na granitse razdela sred”, Izv. RAN. Ser. matematicheskaya, 67:6 (2003), 169–192 | DOI | MR | Zbl

[20] Prokhorov I. V., “O strukture mnozhestva nepreryvnosti resheniya kraevoi zadachi dlya uravneniya perenosa izlucheniya”, Mat. zametki, 86:2 (2009), 256–272 | DOI | MR | Zbl

[21] Kovtanyuk A. E., Prokhorov I. V., “A boundary-value problem for the polarized-radiation transfer equation with Fresnel interface conditions for a layered medium”, J. Comput. Appl. Math., 235:8 (2011), 2006–2014 | DOI | MR | Zbl

[22] Prokhorov I. V., “O razreshimosti nachalno-kraevoi zadachi dlya integrodifferentsialnogo uravneniya”, Sib. mat. zhurn., 53:2 (2012), 377–387 | MR | Zbl

[23] Prokhorov I. V., “Zadacha Koshi dlya uravneniya perenosa izlucheniya s obobschennymi usloviyami sopryazheniya”, Zhurn. vychisl. matematiki i mat. fiziki, 53:5 (2013), 753–766 | DOI | MR | Zbl

[24] Amosov A. A., “Boundary value problem for the radiation transfer equation with reflection and refraction conditions”, J. Math. Sci., 191:2 (2013), 101–149 | DOI | MR | Zbl

[25] Amosov A. A., “Boundary value problem for the radiation transfer equation with diffuse reflection and refraction conditions”, J. Math. Sci., 193:2 (2013), 151–176 | DOI | MR | Zbl

[26] Prokhorov I. V., Suschenko A. A., “O korrektnosti zadachi Koshi dlya uravneniya perenosa izlucheniya s frenelevskimi usloviyami sopryazheniya”, Sib. mat. zhurn., 56:4 (2015), 922–933 | MR | Zbl

[27] Mizokhata C., Teoriya uravnenii s chastnymi proizvodnymi, Mir, M., 1977

[28] Pazy A., Semigroups of linear Operators and Applications to Partial Differential Equations, Applied Mathematics Sciences, 44, Springer-Verl., N.Y., 1983 | DOI | MR | Zbl