The principles of maximum and the methods of statement, boundary value problem for hyperbolic-type and equations of mixed type in bounded simply-connected and multi-connected domain where the boundary is free
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (1996), pp. 5-24.

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M. E. Lerner. The principles of maximum and the methods of statement, boundary value problem for hyperbolic-type and equations of mixed type in bounded simply-connected and multi-connected domain where the boundary is free. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (1996), pp. 5-24. http://geodesic.mathdoc.fr/item/VSGTU_1996_4_a0/

[1] Protter M. H., Weinberger H. F., Maximum principles in differential equations, Prentice-Hall, Inc. X, New Jersey, 1967, 261 pp. | MR | Zbl

[2] Lerner M. E., O printsipakh maksimuma dlya uravnenii giperbolicheskogo tipa i ikh primeneniyakh k uravneniyam smeshannogo tipa, Dis. ... kand. fiz.-mat. nauk, Kuibyshev, 1968, 234 pp.

[3] Sperb R., Maximum principles and their applications, New York, 1984, 224 pp. | MR

[4] Lerner M. E., “O zadache Trikomi s obobschënnymi usloviyami skleivaniya”, DAN SSSR, 218:1 (1974), 24–27 | MR | Zbl

[5] Lerner M. E., “O edinstvennosti reshenii nekotorykh kraevykh zadach so skachkom iskomoi funktsii i eë proizvodnykh na granitse oblasti dlya parabolicheskikh, ellipticheskikh i gipeobolicheskikh uravnenii”, Differentsialnye uravneniya i matematicheskaya fizika, Resp. sb. nauchn. tr., Kuibyshev, 1979, 50–61

[6] Lerner M. E., “Printsipy maksimuma dlya giperbolicheskikh uravnenii v odno- i mnogosvyaznykh oblastyakh pooizvolnoi formy”, Neklassicheskie zadachi uravnenii matematicheskoi fiziki, IM SO AN SSSR, Novosibirsk, 1982, 109–112

[7] Lerner M. E., “Printsipy maksimuma modulya dlya sistem uravnenii s proizvodnymi pervogo i vysokikh poryadkov v mnogomernykh oblastyakh”, Neklassicheskie zadachi uravnenii matematicheskoi fiziki, IM SO AN SSSR, Novosibirsk, 1985, 186–191

[8] Lerner M. E., “Printsipy maksimuma modulya dlya uravnenii giperbolicheskogo i smeshannogo tipov v neklassicheskikh oblastyakh”, DAN SSSR, 287:3 (1986), 550–554 | MR

[9] Lerner M. E., “Printsipy maksimuma dlya giperbolicheskikh uravnenii i sistem uravnenii v neklassicheskikh oblastyakh”, Differents. uravneniya, 22:5 (1986), 848–858 | MR | Zbl

[10] Lerner M. E., “O postanovke i razreshimosti odnogo klassa kraevykh zadach dlya uravneniya Lavrenteva – Bitsadze”, DAN SSSR, 317:3 (1991), 561–565 | MR | Zbl

[11] Lerner M. E., “Ob odnoi zadache dlya modelnogo uravneniya smeshannogo elliptiko-parabolo-giperbolicheskogo tipa s dvusvyaznoi podoblastyu giperbolichnosti”, Differents. uravneniya, 28:8 (1992), 1456–1459 | MR | Zbl

[12] Germain R., “Maximum theorems and reflections of simple waves”, NASA Technical Report, 1955, N 0 3299 | MR

[13] Lerner M. E., “O razreshimosti odnoi kraevoi zadachi dlya giperbolicheskikh uravnenii v neklassicheskikh oblastyakh”, DAN SSSR, 1988

[14] Lerner M. E., “O razreshimosti odnoi kraevoi zadachi dlya giperbolicheskikh uravnenii v neklassicheskikh oblastyakh”, Differents. uravneniya, 25:4 (1989), 704–716 | MR | Zbl

[15] Oleinik O. A., “O svoistvakh reshenii nekotorykh kraevykh zadach uravnenii ellipticheskogo tipa”, Matem. sb., 30(72):13 (1952), 695–702 | MR | Zbl

[16] Kvalvasser V. I., Samarin Yu. P., “Kvaziperiodicheskie i periodicheskie resheniya zadach s podvizhnymi granitsami dlya volnovogo uravneniya v odnomernom prostranstve”, Differents. uravneniya, 11:11 (1966), 1541–1543 | MR

[17] Vytchikov Yu. S., Issledovanie protsessov peredachi tepla v teploobmennykh ustroistvakh pri peremennykh teplofizicheskikh parametrakh, Avtoref. dis. ... kand. tekhn. nauk, Kuibyshev, 1982, 20 pp.

[18] Emets B. V., “Reshenie metodom Rimana zadachi teploobmena pri vozvratno-protivotochnom techenii teplonositelei v rekuperativnykh teploobmennikakh s tselyu optimizatsii ikh raboty”, Modelirovanie i optimizatsiya teploobmena v teploenergetike, Kui­byshev, 1982, 135–137

[19] Emets B. V., Razrabotka matematicheskikh modelei i raschet teploobmena v sverkhglubokikh skvazhinakh s tselyu opredeleniya resursa burilnykh kolonn, Avtoref. dis. ... kand. tekhn. nauk, Kazan, 1986, 13 pp. | Zbl

[20] Lure K. L., Optimalnoe upravlenie v zadachakh matematicheskoi fiziki, Nauka, M., 1976, 478 pp. | MR

[21] Sirazitdinov T. K., Optimizatsiya sistem s raspredelennymi parametrami, Nauka, M., 1977, 479 pp. | MR

[22] Smirnov V. I., Kurs vysshei matematiki, 4, Nauka, M., 1981, 550 pp. | Zbl

[23] Jon F. H., “The Dirichlet problem for a hyperbolic equation”, Amer. Jorn. of Math., 41:1 (1941), 141–154 | DOI | MR

[24] Sobolev S. L., “Primer korrektnoi kraevoi zadachi dlya uravneniya kolebaniya struny s dannymi na vsei granitse oblasti”, DAN SSSR, 109:4 (1956), 707–709 | MR | Zbl

[25] Aleksandryan R. A., “O zadache dlya uravneniya struny i o polnote odnoi sistemy funktsii”, DAN SSSR, XXIII:5 (1950), 869–871 | MR

[26] Berezanskii Yu. M., Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965, 798 pp. | MR

[27] Aleksandryan R. A., Berezanskii Yu. M., Kostyuchenko A. G., “Nekotorye voprosy spektralnoi teorii dlya uravnenii s chastnymi proizvodnymi”, Differentsialnye uravneniya s chastnymi proizvodnymi, Izd-vo MGU, M., 1970, 3–35

[28] Vragov V. N., Kraevye zadachi dlya neklassicheskikh uravnenii matematicheskoi fiziki, IM SO AN SSSR, Novosibirsk, 1983, 84 pp.

[29] Fokin M. V., “O zadache Dirikhle dlya uravneniya kolebaniya struny”, Korrektnye kraevye zadachi dlya neklassicheskikh uravnenii matematicheskoi fiziki, IM SO AN SSSR, Novosibirsk, 1981, 178–181

[30] Fokin M. V., “Ob otsenkakh reshenii nekotorykh kraevykh zadach dlya uravneniya kolebaniya struny”, Neklassicheskie uravneniya matematicheskoi fiziki, IM SO AN SSSR, Novosibirsk, 1983, 151–154

[31] Kalmenov T. Sh., Sadybekov M. A., “O zadache Dirikhle i nelokalnykh kraevykh zada­chakh dlya volnovogo uravneniya”, Differents. uravneniya, 26:1 (1990), 60–65 | MR

[32] Kalmenov T. Sh., O regulyarnykh kraevykh zadachakh i spektre dlya uravnenii giperbolicheskogo i smeshannogo tipov, Avtoref. dis. ... d-ra. fiz.-mat. nauk, MGU, M., 1982, 27 pp.

[33] Lerner M. E., “Printsip maksimuma modulya dlya sistem uravnenii s proizvodnymi pervogo i vysokikh poryadkov v mnogosvyaznykh oblastyakh”, Uravneniya neklassicheskogo tipa, IM SO AN SSSR, Novosibirsk, 1986, 88–92

[34] Sabitov K. B., “O printsipe maksimuma dlya uravnenii smeshannogo tipa”, Differents. uravneniya, 24:11 (1988), 1967–1975 | MR

[35] Sabitov K. B., Nekotorye voprosy kachestvennoi i spektralnoi teorii uravnenii smeshannogo tipa, Avtoref. dis. ... d-ra. fiz.-mat. nauk, In-t matematiki AN USSR, Kiev, 1992, 21 pp.

[36] Lerner M. E., “O dvukh novykh kachestvennykh svoistvakh funktsii Rimana”, DAN SSSR, 307:4 (1989), 807–811 | MR

[37] Lerner M. E., “O kachestvennykh svoistvakh funktsii Rimana”, Differents. urav­neniya, 27:12 (1991), 2106–2120 | MR | Zbl

[38] Frankl F. I., Izbrannye trudy po gazovoi dinamike, Nauka, M., 1973, 711 pp. | MR

[39] Trikomi F., O lineinykh uravneniyakh smeshannogo tipa, Gostekhizdat, M., 1947, 192 pp.

[40] Trikomi F., Lektsii po uravneniyam v chastnykh proizvodnykh, Izd-vo inostr. lit-ry, M., 1957, 442 pp.

[41] Bitsadze A. V., Uravneniya smeshannogo tipa, Izd-vo AN SSSR, M., 1959, 164 pp.

[42] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981, 449 pp. | MR

[43] Babich V. M., Kapilevich M. B. [i dr.], Lineinye uravneniya matematicheskoi fiziki, Nauka, M., 1964, 368 pp. | MR

[44] Smirnov M. M., Uravneniya smeshannogo tipa, Nauka, M., 1970, 295 pp. | MR

[45] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shkola, M., 1985, 304 pp. | MR | Zbl

[46] Salakhitdinov M. S., Uravneniya smeshanno-sostavnogo tipa, FAN, Tashkent, 1974, 156 pp. | MR | Zbl

[47] Dzhuraev T. D., Kraevye zadachi dlya uravnenii smeshannogo i smeshanno-sostavnogo tipa, FAN, Tashkent, 1979, 180 pp. | MR | Zbl

[48] Moiseev E. I., Uravneniya smeshannogo tipa so spektralnym parametrom, Izd-vo MGU, M., 1988, 150 pp. | MR | Zbl

[49] Kuzmin A. G., Neklassicheskie uravneniya smeshannogo tipa i ikh prilozheniya k ga­zovoi dinamike, LGU, L., 1990, 204 pp.

[50] Repin O. A., Kraevye zadachi so smescheniem dlya uravnenii giperbolicheskogo i sme­shannogo tipa, Izd-vo Sarat. un-ta, Saratov, 1992, 161 pp. | MR