Geodesic
Resolvent approach to the Fourier method in a mixed problem for the wave equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 621-630 
V. V. Kornev; A. P. Khromov. Resolvent approach to the Fourier method in a mixed problem for the wave equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 621-630. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The method of contour integration as applied to the resolvent of the spectral problem is used to substantiate the Fourier method in a mixed problem for the wave equation with a complex potential and boundary conditions generalizing free-end boundary conditions. Minimum smoothness assumptions are made about the initial data. Krylov’s technique of accelerating the convergence of the Fourier method is essentially employed.

[1] Steklov V. A., Osnovnye zadachi matematicheskoi fiziki, Nauka, M., 1983, 432 pp.

[2] Petrovskii I. G., Lektsii ob uravneniyakh s chastnymi proizvodnymi, GITTL, M.–L., 1953, 360 pp.

[3] Smirnov V. I., Kurs vysshei matematiki, v 4 t., v. 4, Gostekhizdat, M., 1953, 804 pp.

[4] Ladyzhenskaya O. A., Smeshannaya zadacha dlya giperbolicheskogo uravneniya, Gostekhizdat, M., 1953, 282 pp.

[5] Ilin V. A., Izbrannye trudy, v 2 t., v. 1, Izd-vo OOO “Maks-press”, M., 2008, 727 pp.

[6] Ilin V. A., “O razreshimosti smeshannykh zadach dlya giperbolicheskikh i parabolicheskikh uravnenii”, UMN, 15:2 (1960), 97–154 | MR | Zbl

[7] Chernyatin V. A., Obosnovanie metoda Fure v smeshannoi zadache dlya uravnenii v chastnykh proizvodnykh, Izd-vo Mosk. un-ta, M., 1991, 112 pp.

[8] Krylov A. N., O nekotorykh differentsialnykh uravneniyakh matematicheskoi fiziki, imeyuschikh prilozheniya v tekhnicheskikh voprosakh, GITTL, M.–L., 1950, 368 pp.

[9] Burlutskaya M. Sh., Khromov A. P., “Smeshannye zadachi dlya giperbolicheskikh uravnenii pervogo poryadka s involyutsiei”, Dokl. AN, 441:2 (2011), 151–154

[10] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969, 528 pp. | MR

[11] Rasulov M. L., Metod konturnogo integrala, Nauka, M., 1964, 462 pp. | MR

[12] Vagabov A. I., Vvedenie v spektralnuyu teoriyu differentsialnykh operatorov, Izd-vo Rost. un-ta, Rostov n/D, 1994, 160 pp.

[13] Marchenko V. A., Operatory Shturma–Liuvilya i ikh prilozheniya, Nauk. dumka, Kiev, 1977, 392 pp. | MR

[14] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1971, 538 pp. | MR