Geodesic
Regularization of the Solution of the Cauchy Problem for the System of Maxwell Equations in an Unbounded Domain
Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 445-455

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We study the analytic continuation of the solution of the system of Maxwell equations in a spatial unbounded domain from its values on a part of the boundary of this domain. We construct an approximate solution of this problem based on the Carleman matrix method.
Keywords: Maxwell equations, Cauchy problem, regularization, analytic continuation, Helmholtz equation.
Mots-clés : Carleman matrix, Laplace equation 
È. N. Sattorov. Regularization of the Solution of the Cauchy Problem for the System of Maxwell Equations in an Unbounded Domain. Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 445-455. http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a13/
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[1] Zh. Adamar, Zadacha Koshi dlya lineinykh uravnenii s chastnymi proizvodnymi giperbolicheskogo tipa, Nauka, M., 1978 | MR | Zbl

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

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

[4] M. M. Lavrentev, “O zadache Koshi dlya uravneniya Laplasa”, Izv. AN SSSR. Ser. matem., 20:6 (1956), 819–842 | MR | Zbl

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

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

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

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

[9] Sh. Ya. Yarmukhamedov, T. I. Ishankulov, O. I. Makhmudov, “O zadache Koshi dlya sistemy uravnenii teorii uprugosti v prostranstve”, Sib. matem. zhurn., 33:1 (1992), 186–190 | MR | Zbl

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

[11] E. N. Sattorov, Dzh. Mardonov, “Regulyarizatsiya resheniya zadachi Koshi dlya sistemy uravnenii Maksvella”, Tezisy dokladov mezhdunarodnoi konferentsii “Ill-posed and Classical Problems of Mathematical Physics and Analysis” (Samarakand, Uzbekistan, Sentyabr 11–15, 2000), Samarakandskii gos. un-t, Samarakand, 2000, 77

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

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

[14] J. A. Stratton, L. J. Chu, “Diffraction theory of electromagnetic waves”, Phys. Rev., 56:1 (1939), 99–107 | DOI | Zbl