Geodesic
A mixed boundary value problem for a hyperbolic equation with degenerate principal part
Sbornik. Mathematics, Tome 43 (1982) no. 4, pp. 499-513 
F. T. Baranovskii. A mixed boundary value problem for a hyperbolic equation with degenerate principal part. Sbornik. Mathematics, Tome 43 (1982) no. 4, pp. 499-513. http://geodesic.mathdoc.fr/item/SM_1982_43_4_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a hyperbolic equation with degenerate principal part this paper considers a mixed problem with homogeneous boundary values and modified initial data. Sufficient conditions for its unique solvability are found. Bibliography: 8 titles.

[1] Krasnov M. L., “Smeshannye kraevye zadachi dlya vyrozhdayuschikhsya lineinykh giperbolicheskikh differentsialnykh uravnenii vtorogo poryadka”, Matem. sb., 49 (91) (1959), 29–84 | MR | Zbl

[2] Oleinik O. A., “Zadacha Koshi i kraevaya zadacha dlya giperbolicheskikh uravnenii vtorogo poryadka, vyrozhdayuschikhsya v oblasti i na ee granitse”, DAN SSSR, 169:3 (1966), 525–528 | MR | Zbl

[3] Baranovskii F. T., “Smeshannaya zadacha dlya giperbolicheskogo vyrozhdayuschegosya uravneniya”, Izv. VUZov, Matematika, 1960, no. 3(16), 30–42 | MR | Zbl

[4] Baranovskii F. T., “Differentsialnye svoistva resheniya smeshannoi zadachi dlya silno vyrozhdayuschegosya giperbolicheskogo uravneniya”, Izv. VUZov, Matematika, 1964, no. 3(40), 17–27 | MR | Zbl

[5] Oleinik O. A., Radkevich E. V., Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi, Itogi Nauki, ser. Matematika, Matem. analiz 1969, VINITI, M., 1971 | MR | Zbl

[6] Karapetyan K. I., “O zadache Koshi dlya uravneniya giperbolicheskogo tipa, vyrozhdayuschegosya na nachalnoi ploskosti”, DAN SSSR, 106:6 (1956), 963–966 | MR | Zbl

[7] Baranovskii F. T., “O smeshannoi kraevoi zadache dlya giperbolicheskogo uravneniya s vyrozhdayuscheisya glavnoi chastyu”, DAN SSSR, 237:1 (1977), 13–16 | MR | Zbl

[8] Baranovskii F. T., “Kraevaya zadacha dlya giperbolicheskogo uravneniya s vyrozhdayuscheisya glavnoi chastyu”, Ukr. matem. zh., 31:3 (1979), 227–236 | MR | Zbl