Explicit solution of the mixed problem in anisotropic semispace with brightly expressed vertical permeability for Barenblatt–Zheltov–Kochina equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2012), pp. 75-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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For Barenblatt–Zheltov–Kochina model presentation of filtering of liquids in fissured-porous rocks the explicit solution of the mixed problem in anisotropic semispace with brightly expressed vertical permeability is found by reduction of the considered problem of filtering to the solution of the abstract initial boundary-value problem in Banach space.
Keywords: filtering of liquids in fissured-porous rocks, strongly continuous semi-groups of operators.
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     title = {Explicit solution of the mixed problem in anisotropic semispace with brightly expressed vertical permeability for {Barenblatt{\textendash}Zheltov{\textendash}Kochina} equation},
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Kh. G. Umarov. Explicit solution of the mixed problem in anisotropic semispace with brightly expressed vertical permeability for Barenblatt–Zheltov–Kochina equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2012), pp. 75-99. http://geodesic.mathdoc.fr/item/VSGU_2012_6_a9/

[1] P. Ya. Kochina (otv. red.), Razvitie issledovanii po teorii filtratsii v SSSR (1917–1967), Nauka, M., 1969, 546 pp.

[2] Barenblatt G. I., Entov V. M., Ryzhik V. M., Dvizhenie zhidkostei i gazov v prirodnykh plastakh, Nedra, M., 1984, 211 pp. | MR

[3] Basniev K. S., Kochina I. N., Maksimov V. M., Podzemnaya gidromekhanika, Nauka, M., 1993, 416 pp.

[4] Barenblatt G. I., Zheltov Yu. P., Kochina I. N., “Ob osnovnykh predstavleniyakh teorii filtratsii odnorodnykh zhidkostei v treschinovatykh porodakh”, PMM, 24:5 (1960), 852–864 | MR | Zbl

[5] Maidebor V. N., Osobennosti razrabotki neftyanykh mestorozhdenii s treschinovatymi kollektorami, Nedra, M., 1980, 288 pp.

[6] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, Inostr. lit., M., 1962, 896 pp.

[7] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967, 464 pp. | MR

[8] Umarov Kh. G., “Smeshannaya zadacha v banakhovom prostranstve dlya analoga uravneniya diffuzii, ne razreshennogo otnositelno proizvodnoi po vremeni”, Izvestiya vuzov. Ser.: Matematika, 1992, no. 4, 100–103 | MR | Zbl

[9] Iosida K., Funktsionalnyi analiz, Mir, M., 1967, 624 pp. | MR

[10] Krasnoselskii M. A. i dr., Integralnye operatory v prostranstve summiruemykh funktsii, Nauka, M., 1966, 500 pp.