The Cauchy problem for nonstrictly hyperbolic equations
Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 81-109 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new formal asymptotic solution is constructed for a hyperbolic equation with characteristics of variable multiplicity. Bibliography: 20 titles.
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V. V. Kucherenko; Yu. V. Osipov. The Cauchy problem for nonstrictly hyperbolic equations. Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 81-109. http://geodesic.mathdoc.fr/item/SM_1984_48_1_a4/

[1] Kucherenko V. V., “Asimptotika resheniya zadachi Koshi dlya uravneniya s kompleksnymi kharakteristikami”, Sovremennye problemy matematiki, 8, VINITI, M., 1977, 41–136 | Zbl

[2] Ivrii V. Ya., Petkov V. M., “Neobkhodimye usloviya korrektnosti zadachi Koshi dlya nekotorykh giperbolicheskikh operatorov”, UMN, XXIX:5 (1974), 3–70 | MR

[3] Maslov V. P., Fedoryuk M. V., Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR

[4] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR

[5] Kucherenko V. V., Osipov Yu. V., “Asimptoticheskie resheniya obyknovennykh differentsialnykh uravnenii s vyrozhdayuschimsya simvolom”, Matem. sb., 118 (160) (1982), 74–103 | MR | Zbl

[6] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

[7] Kucherenko V. V., “Asimptotika resheniya sistemy $A(x,ihd_xu)=0$ pri $h \to 0$ v sluchae kharakteristik peremennoi kratnosti”, Izv. AN SSSR. Seriya matem., 38 (1974), 625–662 | Zbl

[8] Maslov V. P., Teoriya vozmuschenii i asimptoticheskie metody, Izd-vo MGU, M., 1965

[9] Buslaev V. S., “Proizvodyaschii integral i kanonicheskii operator Maslova v metode VKB”, Funkts. analiz i ego prilozheniya, 3:3 (1969), 17–31 | MR | Zbl

[10] Khërmander L., “Integralnye operatory Fure”, t. 16, No 1, 2, Matematika (sb. perevodov), 1974

[11] Karasev M. V., Maslov V. P., “Algebry s obschimi perestanovochnymi sootnosheniyami i ikh prilozheniya”, t. 13, Sovremennye problemy matematiki, VINITI, M., 1979, 145–267

[12] Starkov A. S., “Yavlenie vyrozhdeniya i rezonansnye yavleniya v zadachakh rasprostraneniya voln”, Matematicheskie voprosy teorii rasprostraneniya voln. II, Zap. nauchn. semin. LOMI, 104, 1981, 217–227 | MR | Zbl

[13] Marimoto J., “Fundamental solution for a hyperbolic equation with involutive characteristics of variable multiplicity”, Comm. Part. Diff. Eq., 4:6 (1979), 609–643 | DOI | MR

[14] Alinhac S., “A class of hypperbolic operators with double involutive characteristics of Fuchsian type”, Comm. Part. Diff. Eq., 3:10 (1978), 877–905 | DOI | MR | Zbl

[15] Melrose R. B., Ulhman G. A., “Lagrangian intersection and the Cauchy problem”, Comm. Pure Appl. Math., 32:4 (1979), 483–519 | DOI | MR | Zbl

[16] Ulhman G. A., “Parametrices for operators with multiple involutive characteristics”, Comm. Part. Diff. Eq., 4:7 (1979), 736–767 | MR

[17] Nakamura G., Uryu H., “Parametrix of certain weakly hyperbolic operators”, Comm. Part. Diff. Eq., 5:8 (1980), 837–896 | DOI | MR | Zbl

[18] Ludwig D., Granoff B., “Propagation of singularities along characteristics with nonuniform multiplicity”, J. Math. Anal. Appl., 21:3 (1968) | DOI | MR

[19] Yoshikawa A., “Construction of a parametrix for a Cauchy problem of some weakly hyperbolic equations. I”, Hokkaido Math. J., 6:2 (1977), 313–344 | MR | Zbl

[20] Yoshikawa A., “Construction of a parametrix for a Cauchy problem of some weakly hyperbolic equations. II, III”, Hokkaido Math. J., 7:1 (1978), 1–26, 127–141 | MR | Zbl