Geodesic
The Cauchy problem of the moment elasticity theory in~$\mathbf R^m$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 30-37.

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In this paper we consider the problem of analytical continuation of the solution to the system of equations of the moment theory of elasticity in spatial many-dimensional domain. We give an explicit formula of restoring of solution inside the domain by values of sought-for solution and values of strains on part of the boundary of this domain.
Keywords: Cauchy problem, Carleman function, system of elacticity theory.
Mots-clés : Carleman matrix 
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I. E. Niyozov; O. I. Makhmudov. The Cauchy problem of the moment elasticity theory in~$\mathbf R^m$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 30-37. http://geodesic.mathdoc.fr/item/IVM_2014_2_a3/

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

[2] Petrovskii I. G., Lektsii ob uravneniyakh s chastnymi proizvodnymi, M., 1961 | MR

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

[4] Makhmudov O. I., Niëzov I. E., “Zadacha Koshi dlya sistemy uravnenii ustanovivshikhsya kolebanii momentnoi teorii uprugosti”, Uzb. matem. zhurn., 2008, no. 4, 104–115 | MR

[5] Makhmudov O. I., Niyozov I. E., Tarkhanov N., “The Cauchy problem of couple-stress elasticity”, Contemporary Mathem. (AMS), 455 (2008), 297–310 | DOI | MR | Zbl

[6] Makhmudov O. I., Niyozov I. E., “The Cauchy problem for the Lame system in infinite domains in $R^m$”, J. Inverse and Ill-posed probl., 14:9 (2006), 905–924 | MR | Zbl

[7] Makhmudov O. I., Niëzov I. E., “O zadache Koshi dlya mnogomernoi sistemy uravnenii Lame”, Izv. vuzov. Matem., 2006, no. 4, 41–50 | MR | Zbl

[8] Makhmudov O. I., Niyozov I. E., “Regularization of a solution to the Cauchy problem for the system of thermoelasticity”, Contemporary Mathem. (AMS), 382 (2005), 285–289 | DOI | MR | Zbl

[9] Makhmudov O. I., Niëzov I. E., “Regulyarizatsiya resheniya zadachi Koshi dlya sistemy teorii uprugosti v beskonechnoi oblasti”, Matem. zametki, 68:4 (2000), 548–553 | DOI | MR | Zbl

[10] Makhmudov O. I., Niyozov I. E., “Regularization of a solutions to the Cauchy problem for systems of elasticity theory”, More progresses on Analysis, Proceedings of the International 5th ISAAK Congress, ed. H. G. W. Begehr, Singapore, 2009, 69–84 | DOI

[11] Aleksidze M. A., Fundamentalnye funktsii v priblizhennykh resheniyakh granichnykh zadach, M., 1991 | MR