Geodesic
Application of the method of generalized potentials to the solution of certain problems in the theory of the diffraction and propagation of waves
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 1081-1092 
Yu. V. Shestopalov. Application of the method of generalized potentials to the solution of certain problems in the theory of the diffraction and propagation of waves. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 7, pp. 1081-1092. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_7_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The nature of the singularities of the limiting values of the derivatives of generalized two-dimensional single and double layer potentials on the boundaries of contours of a certain type has been studied. Applications of the method of generalized potentials to the solution of boundary-value problems for the Helmholtz equation, which arise in the theory of the diffraction and propagation of waves, are considered.

[1] Bitsadze A. V., Uravneniya matematicheskoi fiziki, Nauka, M., 1976 | MR

[2] Khenl X., Maue A., Vestpfal K., Teoriya difraktsii, Mir, M., 1964

[3] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Fizmatgiz, M., 1962

[4] Gyunter N. M., Teoriya potentsiala, Gostekhteorizdat, M., 1953 | MR

[5] Mizokhata S., Teoriya uravnenii s chastnymi proizvodnymi, Mir, M., 1977

[6] Muravei L. A., “Analiticheskoe prodolzhenie po parametru funktsii Grina vneshnikh kraevykh zadach dlya dvumernogo uravneniya Gelmgoltsa”, Matem. sb., 105:1 (1978), 63–108 | MR | Zbl

[7] Panasyuk V. V., Savruk M. P., Nazarchuk Z. T., Metod singulyarnykh integralnykh uravnenii v dvumernykh zadachakh difraktsii, Nauk. dumka, Kiev, 1984 | MR

[8] Shestopalov V. P., Summatornye uravneniya v sovremennoi teorii difraktsii, Nauk. dumka, Kiev, 1983 | MR

[9] Tuchkin Yu. A., “Rasseyanie voln nezamknutymi tsilindricheskimi ekranami proizvolnogo profilya s granichnymi usloviyami Dirikhle”, Dokl. AN SSSR, 285:6 (1985), 1370–1373 | MR

[10] Shestopalov Yu. V., “Sobstvennye volny otkrytykh i ekranirovannykh schelevykh linii, obrazovannykh oblastyami proizvolnogo poperechnogo secheniya”, Dokl. AN SSSR, 289:4 (1986), 840–845 | MR

[11] Ilinskii A. S., Shestopalov Yu. V., Primenenie metodov spektralnoi teorii v zadachakh rasprostraneniya voln, Izd-vo MGU, M., 1989

[12] Sologub V. G., “O reshenii odnogo integralnogo uravneniya tipa svertki s konechnymi predelami integrirovaniya”, Zh. vychisl. matem. i matem. fiz., 11:4 (1971), 837–854 | MR | Zbl

[13] Ilinskii A. S., Galishnikova T. N., “Issledovanie zadach difraktsii v volnovodakh metodom integralnykh uravnenii Fredgolma”, Vychisl. metody i programmirovanie, XX, Izd-vo MGU, M., 1973, 22–37

[14] Repin V. M., “Chislennyi metod resheniya zadachi ob elektromagnitnoi svyazi ob'emov cherez otverstiya”, Zh. vychisl. matem. i matem. fiz., 11:1 (1971), 152–163 | MR

[15] Ilinskii A. S., Shestopalov Yu. V., “Difraktsiya na scheli v idealno provodyaschem ploskom ekrane, lezhaschem na granitse razdela sred”, Vychisl. metody i programmirovanie, XXVIII, Izd-vo MGU, M., 1978, 70–89

[16] Sanches-Palensiya E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984 | MR