Abstract:
In this paper, we investigate the analytic continuation of the solution of the system of Lamé equations in a bounded space domain from the values of the solution and the stress values on part of the boundary of this domain, i.e., a Cauchy problem is studied. We construct an approximate solution of this problem based on the Carleman matrix method.
system of elliptic differential equations
Citation:
O. I. Makhmudov, “Cauchy Problem for Elliptic Systems in the Space Rm”, Mat. Zametki, 75:6 (2004), 849–860; Math. Notes, 75:6 (2004), 794–804
\Bibitem{Mak04}
\by O.~I.~Makhmudov
\paper Cauchy Problem for Elliptic Systems in the Space $\mathbb R^m$
\jour Mat. Zametki
\yr 2004
\vol 75
\issue 6
\pages 849--860
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\crossref{https://doi.org/10.4213/mzm76}
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\transl
\jour Math. Notes
\yr 2004
\vol 75
\issue 6
\pages 794--804
\crossref{https://doi.org/10.1023/B:MATN.0000030989.78008.a7}
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Linking options:
https://www.mathnet.ru/eng/mzm76
https://doi.org/10.4213/mzm76
https://www.mathnet.ru/eng/mzm/v75/i6/p849
This publication is cited in the following 4 articles:
Makhmudo K.O., Makhmudov O.I., Tarkhanov N., “Equations of Maxwell type”, J Math Anal Appl, 378:1 (2011), 64–75
E. V. Arbuzov, A. L. Bukhgeim, “O reshenii zadachi Koshi dlya ellipticheskikh uravnenii vtorogo poryadka na ploskosti s pomoschyu integralnogo operatora Koshi”, Sib. elektron. matem. izv., 7 (2010), 173–177
E. V. Arbuzov, A. L. Bukhgeim, “Formula Karlemana dlya sistemy uravnenii elektrodinamiki na ploskosti [Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke”]”, Sib. elektron. matem. izv., 5 (2008), 448–455
È. V. Arbuzov, A. L. Bukhgeim, “The Carleman formula for the Helmholtz equation on the plane”, Siberian Math. J., 47:3 (2006), 425–432