Geodesic
Explicit solution of the mixed problem in an anisotropic half-space for the Barenblatt–Zheltov–Kochina equation
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 1, pp. 51-64 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the Barenblatt–Zheltov–Kochina model of filtering liquids in fissured rocks an explicit solution of the mixed problem in anisotropic half-space with pronounced horizontal permeability is found by reduction to some abstract mixed problem in Banach space. 
@article{VMJ_2013_15_1_a6,
     author = {Kh. G. Umarov},
     title = {Explicit solution of the mixed problem in an anisotropic half-space for the {Barenblatt{\textendash}Zheltov{\textendash}Kochina} equation},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {51--64},
     year = {2013},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a6/}
}
TY  - JOUR
AU  - Kh. G. Umarov
TI  - Explicit solution of the mixed problem in an anisotropic half-space for the Barenblatt–Zheltov–Kochina equation
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2013
SP  - 51
EP  - 64
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a6/
LA  - ru
ID  - VMJ_2013_15_1_a6
ER  - 
%0 Journal Article
%A Kh. G. Umarov
%T Explicit solution of the mixed problem in an anisotropic half-space for the Barenblatt–Zheltov–Kochina equation
%J Vladikavkazskij matematičeskij žurnal
%D 2013
%P 51-64
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a6/
%G ru
%F VMJ_2013_15_1_a6
Kh. G. Umarov. Explicit solution of the mixed problem in an anisotropic half-space for the Barenblatt–Zheltov–Kochina equation. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 1, pp. 51-64. http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a6/

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

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

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

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

[5] Polubarinova-Kochina P. Ya., Teoriya dvizheniya gruntovykh vod, Nauka, M., 1977, 664 pp. | MR

[6] Butzer R. Z., Berens H., Semi-Groups of Operators and Approximation, Springer, Berlin, 1967, 318 pp. | MR | Zbl

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

[8] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, Izd-vo inostr. lit., M., 1962, 896 pp.

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

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

[11] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966, 500 pp. | MR | Zbl