Regularization in inverse dynamic problems for the equation of $SH$-waves in a porous medium
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 45-57 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Regularization algorithms for dynamic inverse problems for 1D equation of $SH$-waves in fluid saturated of porous media with energy dissipation at intercomponent friction have been constructed.
@article{VMJ_2013_15_2_a5,
     author = {Kh. Kh. Imomnazarov and Sh. Kh. Imomnazarov and T. T. Rakhmonov and Z. Sh. Yangiboyev},
     title = {Regularization in inverse dynamic problems for the equation of $SH$-waves in a~porous medium},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {45--57},
     year = {2013},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a5/}
}
TY  - JOUR
AU  - Kh. Kh. Imomnazarov
AU  - Sh. Kh. Imomnazarov
AU  - T. T. Rakhmonov
AU  - Z. Sh. Yangiboyev
TI  - Regularization in inverse dynamic problems for the equation of $SH$-waves in a porous medium
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2013
SP  - 45
EP  - 57
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a5/
LA  - ru
ID  - VMJ_2013_15_2_a5
ER  - 
%0 Journal Article
%A Kh. Kh. Imomnazarov
%A Sh. Kh. Imomnazarov
%A T. T. Rakhmonov
%A Z. Sh. Yangiboyev
%T Regularization in inverse dynamic problems for the equation of $SH$-waves in a porous medium
%J Vladikavkazskij matematičeskij žurnal
%D 2013
%P 45-57
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a5/
%G ru
%F VMJ_2013_15_2_a5
Kh. Kh. Imomnazarov; Sh. Kh. Imomnazarov; T. T. Rakhmonov; Z. Sh. Yangiboyev. Regularization in inverse dynamic problems for the equation of $SH$-waves in a porous medium. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 45-57. http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a5/

[1] Nuzhin M. T., Ilinskii N. B., Metody postroeniya podzemnogo kontura gidrotekhnicheskikh sooruzhenii. Obratnye kraevye zadachi teorii filtratsii, KGU, Kazan, 1963, 140 pp.

[2] Frenkel Ya. I., “K teorii seismicheskikh i seismoelektricheskikh yavlenii vo vlazhnoi pochve”, Izv. AN SSSR. Ser. Geografiya i geofizika, 8:4 (1944), 133–150 | MR | Zbl

[3] Biot M. A., “Theory of propagation of elastic waves in fluid-saturated porous solid. I. Low-frequency range”, The J. of the Acoustical Society of America, 28:2 (1956), 168–178 | DOI | MR

[4] Roberts P. H., Loper D. E., “Dynamical processes in slurries”, Structure and Dynamics of Partially Solidified System. NATO ASI. Serie E, 125 (1987), 229–290 | DOI

[5] Dorovskii V. N., “Kontinualnaya teoriya filtratsii”, Geologiya i geofizika, 1989, no. 7, 39–45

[6] Dorovskii V. N., Perepechko Yu. V., “Fenomenologicheskoe opisanie dvukhskorostnoi sredy s relaksiruyuschimi kasatelnymi napryazheniyami”, PMTF, 33:3 (1992), 403–409 | MR

[7] Alekseev A. S., “Obratnye dinamicheskie zadachi seismiki”, Nekotorye metody i algoritmy interpretatsii geofizicheskikh dannykh, Nauka, M., 1967, 9–84

[8] Alekseev A. S., “Nekotorye obratnye zadachi teorii rasprostraneniya voln”, Izv. AN SSSR. Ser. Geofizika, 1962, no. 11, 1514–1531

[9] Gelfand I. M., Levitan B. M., “Ob opredelenii differentsialnogo uravneniya po ego spektralnoi funktsii”, Izv. AN SSSR. Ser. Matematika, 15:4 (1951), 309–360 | MR | Zbl

[10] Krein M. G., “Reshenie obratnoi zadachi Shturma–Liuvillya”, Dokl. AN SSSR, 76:1 (1951), 21–24 | MR

[11] Krein M. G., “Ob odnom metode effektivnogo resheniya obratnoi kraevoi zadachi”, Dokl. AN SSSR, 94:6 (1954), 987–990 | MR

[12] Alekseev A. S., Dobrinskii V. I., “Nekotorye voprosy prakticheskogo ispolzovaniya obratnykh dinamicheskikh zadach seismiki”, Mat. problemy geofiziki, 6, ch. 2, VTs SO AN SSSR, Novosibirsk, 1975, 7–53

[13] Romanov V. G., Obratnye zadachi matematicheskoi fiziki, Nauka, M., 1984, 261 pp. | MR

[14] Belishev M. I., Blagoveschinskii A. S., Dinamicheskie obratnye zadachi teorii voln, Izd-vo SPbGU, SPb., 1999, 268 pp.

[15] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1986, 287 pp. | MR

[16] Lavrentev M. M., Romanov V. G., Shishatskii S. P., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980, 286 pp. | MR

[17] Alekseev A. S., Imomnazarov Kh. Kh., Grachev E. V., Rakhmonov T. T., Imomnazarov B. Kh., “Pryamye i obratnye dinamicheskie zadachi dlya sistemy uravnenii kontinualnoi teorii filtratsii”, Sib. zhur. industrialnoi matematiki, 7:1(17) (2004), 3–8 | Zbl

[18] Imomnazarov Kh. Kh., “Estimates of conditional stability of some combined inverse problems for Maxwell's equations and equations of porous media”, Comp. Appl. Math., 20 (2001), 20–34 | MR

[19] Imomnazarov Kh. Kh., “Chislennoe modelirovanie nekotorykh zadach teorii filtratsii dlya poristykh sred”, Sib. zhur. industrialnoi matematiki, 4:2(8) (2001), 154–165 | MR | Zbl

[20] Bukhgeim A. L., Uravneniya Volterra i obratnye zadachi, Nauka, Novosibirsk, 1983, 207 pp. | MR

[21] Imomnazarov Kh. Kh., Kholmurodov A. E., “Pryamye i obratnye dinamicheskie zadachi dlya uravneniya SH voln v poristoi srede”, Vestn. NUUZ. Ser. Mekhanika i matematika, 2006, no. 2, 86–91 | MR

[22] Imomnazarov Kh. Kh., Kholmurodov A. E., “Direct and inverse dynamic problems for SH-waves in porous media”, Math. and Computer Modelling, 45:3–4 (2007), 270–280 | DOI | MR | Zbl

[23] Pestov L. N., “Ob odnom sposobe regulyarizatsii odnomernoi zadachi teorii uprugosti”, Mat. modelirovanie v geofizike, Tr. VTs SO RAN, 1, Novosibirsk, 1993, 112–124

[24] Dorovskii V. N., Perepechko Yu. V., Romenskii E. I., “Volnovye protsessy v nasyschennykh poristykh uprugodeformirunmykh sredakh”, FGV, 1993, no. 1, 100–111

[25] Blokhin A. M., Dorovsky V. N., Mathematical modelling in the theory of multivelocity continuum, Nova Science Publishers Inc., New York, 1995, 192 pp. | MR

[26] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1968, 496 pp. | MR | Zbl

[27] Bukhgeim A. L., Raznostnye metody resheniya nekorrektnykh zadach, VTs SO AN SSSR, Novosibirsk, 1986, 149 pp. | MR