Geodesic
Reconstruction of solutions to a~generalized Moisil--Teodorescu system in a~spatial domain from their values on a~part of the boundary
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2011), pp. 72-84.

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In this paper we consider the problem of reconstructing solutions to a generalized Moisil–Teodorescu system in a spatial domain from their values on a part of the domain boundary, i.e., the Cauchy problem. We construct an approximate solution to this problem with the help of the Carleman matrix method.
Keywords: generalized Moisil–Teodorescu system, ill-posed problems, regularized solution, approximate solution
Mots-clés : Carleman matrix. 
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E. N. Sattorov. Reconstruction of solutions to a~generalized Moisil--Teodorescu system in a~spatial domain from their values on a~part of the boundary. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2011), pp. 72-84. http://geodesic.mathdoc.fr/item/IVM_2011_1_a6/

[1] Obolashvili E. I., “Prostranstvennye obobschennye golomorfnye vektory”, Differents. uravneniya, 11:1 (1975), 108–115

[2] Moisil Gr. C., Theodorescu N., “Fonctions holomorphes dans l'espace”, Mathematica, 5 (1931), 142–159 | Zbl

[3] Bitsadze A. V., Kraevye zadachi dlya ellipticheskikh uravnenii vtorogo poryadka, Nauka, M., 1966 | Zbl

[4] Brackx F., Delanghe K., Sommen F., Clifford analysis, Research Notes in Mathematics, 76, Pitman, Advanced Publ. Program, Boston–London–Melbourn, 1982 | MR | Zbl

[5] Vladimirov V. S., Volovich I. V., “Superanaliz. I. Differentsialnoe ischislenie”, TMF, 59:1 (1984), 3–27 | MR | Zbl

[6] Vladimirov V. S., Volovich I. V., “Superanaliz. II. Integralnoe ischislenie”, TMF, 60:2 (1984), 169–198 | MR | Zbl

[7] Adamar Zh., Zadacha Koshi dlya lineinykh uravnenii s chastnymi proizvodnymi giperbolicheskogo tipa, Nauka, M., 1978 | MR

[8] Aizenberg L. A., Formuly Karlemana v kompleksnom analize. Pervye prilozheniya, Nauka, Novosibirsk, 1990 | MR

[9] Tarkhanov N. N., The Cauchy problem for solutions of elliptic equations, Mathematical toplics, 7, Akad. Verl., Berlin, 1995 | MR | Zbl

[10] Lavrentev M. M., O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki, VTs SO AN SSSR, Novosibirsk, 1962 | MR

[11] Bers A., Dzhon F., Shekhter M., Uravneniya s chastnymi proizvodnymi, Mir, M., 1966 | MR | Zbl

[12] Yarmukhamedov Sh. Ya., “O zadache Koshi dlya uravneniya Laplasa”, DAN SSSR, 235:2 (1977), 281–283 | MR | Zbl

[13] Lavrentev M. M., “O zadache Koshi dlya lineinykh ellipticheskikh uravnenii vtorogo poryadka”, DAN SSSR, 112:2 (1957), 195–197 | MR

[14] Mergelyan S. N., “Garmonicheskaya approksimatsiya i priblizhennoe reshenie zadachi Koshi dlya uravneniya Laplasa”, UMN, 11:5 (1956), 3–26 | MR | Zbl

[15] Ivanov V. K., “Zadacha Koshi dlya uravneniya Laplasa v beskonechnoi polose”, Differents. uravneniya, 1:1 (1965), 131–136 | Zbl

[16] Yarmukhamedov Sh. Ya., “O prodolzhenii resheniya uravneniya Gelmgoltsa”, Dokl. RAN, 357:3 (1997), 320–323 | MR | Zbl

[17] Yarmukhamedov Sh., “Ob analiticheskom prodolzhenii golomorfnogo vektora po ego granichnym znacheniyam na kuske granitsy”, Izv. AN UzbSSR. Ser. fiz.-matem. nauk, 1980, no. 6, 34–40 | MR | Zbl

[18] Aizenberg L. A., Tarkhanov N. N., “Abstraktnaya formula Karlemana”, DAN SSSR, 298:6 (1988), 1292–1296 | MR

[19] Makhmudov O. I., “Zadacha Koshi dlya sistemy uravnenii teorii uprugosti i termouprugosti v prostranstve”, Izv. vuzov. Matematika, 2004, no. 2, 43–53 | MR | Zbl

[20] Sattorov E. N., Mardonov Dzh. A., “Zadacha Koshi dlya sistemy uravnenii Maksvella”, Sib. matem. zhurn., 44:4 (2003), 851–861 | MR | Zbl

[21] Sattorov E. N., “Regulyarizatsiya resheniya zadachi Koshi dlya obobschennoi sistemy Moisila–Teodoresku”, Differents. uravneniya, 44:8 (2008), 1100–1110 | MR | Zbl

[22] Sattorov E. N., “O prodolzhenii resheniya odnorodnoi sistemy uravnenii Maksvella”, Izv. vuzov. Matematika, 2008, no. 8, 78–83 | MR | Zbl

[23] Marchuk N. G., Gauge fields of the matrix Dirac equation, 23 Nov., 1998, arXiv: math-ph/9811021v1 | MR

[24] Tikhonov A. N., “O reshenii nekorrektno postavlennykh zadach i metode regulyarizatsii”, DAN SSSR, 151:3 (1963), 501–504 | MR | Zbl

[25] Tarkhanov N. N., “O matritse Karlemana dlya ellipticheskikh sistem”, DAN SSSR, 284:2 (1985), 294–297 | MR | Zbl

[26] Ishankulov T., “Continuation of the solution to the Moisil–Theodorescu's system of equations”, International conference “Ill-posed and inverse problems” (August 5–9, 2002), Novosibirsk

[27] Vekua I. N., Obobschennye analiticheskie funktsii, Fizmatlit, M., 1988 | MR

[28] Ishankulov T. I., “O vozmozhnosti obobschenno-analiticheskogo prodolzheniya v oblast funktsii, zadannykh na kuske ee granitsy”, Sib. matem. zhurn., 41:6 (2000), 1350–1356 | MR | Zbl

[29] Sattorov E. N., “Ob analiticheskom prodolzhenii obobschenno analiticheskikh funktsii v prostranstvennoi oblasti po ikh granichnym znacheniyam na kuske granitsy”, Uzbekskii matem. zhurn., 2007, no. 1, 97–105 | MR | Zbl