The correctness of the Cauchy--Goursat problem for loaded degenerate hyperbolic equations in some special cases, and its equivalent to the problem with nonlocal boundary conditions

E. N. Ogorodnikov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 26 (2004), pp. 26-38.

Bibliographie

[1] Bitsadze A. V., “K teorii odnogo klassa uravnenii smeshannogo tipa”, Nekotorye problemy matematiki i mekhaniki, Nauka, M.-L., 1970, 112–119

[2] Bitsadze A. V., “K teorii uravnenii smeshannogo tipa, poryadok kotorykh vyrozhdaetsya vdol linii izmeneniya tipa”, Mekhanika sploshnoi sredy i rodstvennye problemy analiza, Nauka, M., 1972, 47–52 | MR

[3] Nakhushev A. M., “O zadache Darbu dlya giperbolicheskikh uravnenii”, DAN SSSR, 195:4 (1970), 776–779 | Zbl

[4] Nakhushev A. M., “O zadache Darbu dlya vyrozhdayuschikhsya giperbolicheskikh uravnenii”, Differents. uravneniya, 7:1 (1971), 103–108 | MR

[5] Nakhushev A. M., “Kriterii edinstvennosti resheniya zadachi Darbu dlya odnogo vyrozhdayuschegosya giperbolicheskogo uravneniya vlagoperenosa”, Differents. uravneniya, 16:9 (1980), 1643–1649 | MR | Zbl

[6] Andreev A. A., Ogorodnikov E. N., “O korrektnosti zadach Darbu i Koshi–Gursa dlya odnoi vyrozhdayuscheisya giperbolicheskoi sistemy”, Matematicheskoe modelirovanie i kraevye zadachi, Trudy vosmoi mezhvuz. konferentsii. Chast 3, SamGTU, Samara, 1998, 3–7

[7] Ogorodnikov E. N., “O nekotorykh kraevykh zadachakh dlya sistemy uravnenii tipa Bitsadze–Lykova s involyutivnoi matritsei”, Matematicheskoe modelirovanie i kraevye zadachi, Trudy desyatoi mezhvuz. konferentsii. Chast 3, SamGTU, Samara, 2000, 119–126

[8] Andreev A. A., Ogorodnikov E. N., “Nekotorye lokalnye i nelokalnye analogi zadachi Koshi–Gursa dlya sistemy uravnenii tipa Bitsadze–Lykova s involyutivnoi matritsei”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 16 (2002), 19–35 | DOI

[9] Bitsadze A. V., Uravneniya smeshannogo tipa, AN SSSR, M., 1959

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

[11] Andreev A. A., “Ob odnom klasse sistem differentsialnykh uravnenii giperbolicheskogo tipa”, Differents. uravneniya, Sb. trudov matem. kafedr pedinst-ov RSFSR, 16, RGPI, Ryazan, 1980, 3–5

[12] Andreev A. A., “O metode Rimana dlya odnoi sistemy uravnenii giperbolicheskogo tipa s kratnymi kharakteristikami”, Korrektnye kraevye zadachi dlya neklassicheskikh uravnenii matematicheskoi fiziki, IM SOAN SSSR, Novosibirsk, 1981, 13–16

[13] Andreev A. A., “Zadachi Koshi–Gursa i Darbu dlya sistem uravnenii Eilera–Puassona–Darbu (EPD)”, Differents. uravneniya s chastnymi proizvodnymi, Mezhvuz. sb. nauchn. trudov, KGPI, Kuibyshev, 1983, 53–57

[14] Andreev A. A., Postroenie elementarnykh reshenii i reshenie zadachi Koshi dlya uravnenii i sistem uravnenii giperbolicheskogo tipa, Dis. ... kand. fiz.-mat. nauk, Kuibyshev, 1981

[15] Andreev A. A., “Zadacha Koshi dlya nekotorykh vyrozhdayuschikhsya giperbolicheskikh sistem vtorogo i chetvertogo poryadka”, Differents. i integralnye uravneniya, Mezhvuz. sb. nauchn. trudov, KGPI, Kuibyshev, 1987, 46–57

[16] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967 | MR

[17] Andreev A. A., Kilbas A. A., “O nekotorykh assotsiirovannykh giperbolicheskikh funktsiyakh”, Izv. vyssh. ucheb. zavedenii. Matem., 1984, no. 12, 3–12 | MR | Zbl

[18] Andreev A. A., “O nekotorykh prilozheniyakh assotsiirovannykh gipergeometricheskikh funktsii”, Differents. uravneniya (matem. fizika), Tezisy dokl. uchastnikov Kuibyshevskogo oblast. mezhvuz. nauchn. soveschaniya-seminara, KGPI, Kuibyshev, 1984, 8–9

[19] Andreev A. A., Senitskii A. Yu., “O zadache Koshi dlya sistemy vyrozhdayuschikhsya uravnenii tipa Lykova”, Neklassicheskie differentsialnye uravneniya v chastnykh proizvodnykh, IM SOAN SSSR, Novosibirsk, 1988, 105–107

[20] Ogorodnikov E. N., “O korrektnosti nekotorykh nelokalnykh kraevykh zadach dlya sistemy uravnenii Bitsadze–Lykova s involyutivnoi matritsei”, Matem. modelirovanie i kraevye zadachi, Trudy devyatoi mezhvuz. konferentsii, SamGTU, Samara, 1999, 97–102

[21] Andreev A. A., Ogorodnikov E. N., “Nekotorye kraevye zadachi s usloviem tipa Bitsadze–Samarskogo dlya sistemy uravnenii s operatorom Bitsadze–Lykova”, Matem. modelirovanie i kraevye zadachi, Trudy devyatoi mezhvuz. konferentsii, SamGTU, Samara, 1999, 3–11

[22] Ogorodnikov E. N., Nelokalnye kraevye zadachi dlya odnoi vyrozhdayuscheisya sistemy giperbolicheskogo tipa vtorogo poryadka s kratnymi kharakteristikami, Dis. ... kand. fiz.-mat. nauk, Samara, 2000

[23] Andreev A. A., Ogorodnikov E. N., “Kraevaya zadacha so smescheniem dlya sistemy uravnenii s vyrozhdeniem poryadka v nekotorykh spetsialnykh sluchayakh”, Matem. modelirovanie i kraevye zadachi, Trudy odinnadtsatoi mezhvuz. konferentsii. Chast 3, SamGTU, Samara, 2001, 3–10

[24] Andreev A. A., Ogorodnikov E. N., “O korrektnosti nelokalnykh analogov zadachi Koshi–Gursa dlya sistemy uravnenii s vyrozhdeniem poryadka v odnom spetsialnom sluchae”, Problemy sovremennoi matematiki, Materialy nauchn. konferentsii. Kazan. matem. obschestvo, Trudy matemat. tsentra im. Lobachevskogo, 11, Unipres, Kazan, 2001, 10–14

[25] Ogorodnikov E. N., “Korrektnost zadach Koshi–Gursa i ikh svyaz s nelokalnymi kraevymi zadachami dlya odnoi modelnoi sistemy vyrozhdayuschikhsya nagruzhennykh giperbolicheskikh uravnenii s involyutivnoi matritsei”, Matem modelirovanie i kraevye zadachi, Trudy dvenadtsatoi mezhvuz. konferentsii. Chast 3, SamGTU, Samara, 2002, 132–139

[26] Samko S. G., Kilbas A. A., Marichev O.I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987 | MR | Zbl

[27] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. T. 1. Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Nauka, M., 1973

[28] Dzhbrshyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[29] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. T. 3. Ellipticheskie i avtomorfnye funktsii. Funktsii Lame i Mate, Nauka, M., 1967 | MR

[30] Pskhu A. V., “Reshenie kraevoi zadachi dlya differentsialnogo uravneniya s chastnymi proizvodnymi drobnogo poryadka”, Dokl. Adygeiskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 5:1 (2000), 45–53

[31] Prabhakar T. R., “A singular integral equation with a generalized Mittag-Leffler function in the kernel”, Yokohama Math. I, 19 (1971), 7–15 | MR | Zbl

[32] Hille E., Tamarkin I. D., “On the theory of linear integral equations”, Ann. Math., 31 (1930), 479–528 | DOI | MR | Zbl

[33] Nakhushev A. M., “O nelokalnykh kraevykh zadachakh so smescheniem i ikh svyazi s nagruzhennymi uravneniyami”, Differents. uravneniya, 21:1 (1985), 92–101 | MR | Zbl