Geodesic
Boundary Value Problems for Quasi-Hyperbolic Equations with Degeneration
Matematičeskie zametki, Tome 112 (2022) no. 6, pp. 825-838.

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The paper deals with the solvability analysis of boundary value problems for degenerate higher-order quasi-hyperbolic equations. The problems in question have the specific feature that the manifolds on which the equations characteristically degenerate are not freed from carrying boundary data. The aim of this paper is to prove the existence and uniqueness of regular solutions of the problems under study, that is, solutions all of whose generalized derivatives occurring in the corresponding equations exist as generalized derivatives in the sense of Sobolev.
Keywords: quasi-hyperbolic equation, degeneration, boundary value problem, regular solution, uniqueness.
Mots-clés : existence 
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A. I. Kozhanov; N. R. Spiridonova. Boundary Value Problems for Quasi-Hyperbolic Equations with Degeneration. Matematičeskie zametki, Tome 112 (2022) no. 6, pp. 825-838. http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a3/

[1] H. O. Fattorini, “The underdetermined Cauchy problem in Banach spaces”, Math. Ann., 200 (1973), 103–112 | DOI | MR | Zbl

[2] H. O. Fattorini, “Two point boundary value problems for operational differential equations”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 1 (1974), 63–79 | MR

[3] A. I. Kozhanov, N. R. Pinigina, “Kraevye zadachi dlya nekotorykh neklassicheskikh differentsialnykh uravnenii vysokogo poryadka”, Matem. zametki, 101:3 (2017), 403–412 | DOI | MR | Zbl

[4] V. N. Vragov, “K teorii kraevykh zadach dlya uravnenii smeshannogo tipa v prostranstve”, Differents. uravneniya, 13:6 (1977), 1098–1105 | MR | Zbl

[5] V. N. Vragov, “O postanovke i razreshimosti kraevykh zadach dlya uravnenii smeshanno-sostavnogo tipa”, Matem. analiz i smezhnye voprosy matematiki, Nauka, Novosibirsk, 1978, 5–13

[6] I. E. Egorov, V. E. Fedorov, Neklassicheskie uravneniya matematicheskoi fiziki vysokogo poryadka, Izd-vo VTs SO RAN, Novosibirsk, 1995 | MR

[7] I. E. Egorov, V. E. Fedorov, I. M. Tikhonova, E. S. Efimova, “The Galerkin method for nonclassical equations of mathematical physics”, AIP Conf. Proc., 1907 (2017), Paper No. 020011 | DOI

[8] I. E. Egorov, “O kraevoi zadache dlya uravneniya smeshannogo tipa so spektralnym parametrom”, Matem. zametki SVFU, 21:1 (2014), 11–17 | MR | Zbl

[9] A. I. Kozhanov, B. D. Koshanov, Zh. B. Sultangazieva, “Novye kraevye zadachi dlya kvazigiperbolicheskikh uravnenii chetvertogo poryadka”, Sib. elektron. matem. izv., 16 (2019), 1410–1436 | DOI | MR | Zbl

[10] M. V. Keldysh, “O nekotorykh sluchayakh vyrozhdeniya uravnenii ellipticheskogo tipa na granitse oblasti”, Dokl. AN SSSR, 77:2 (1951), 181–183 | Zbl

[11] M. M. Smirnov, Vyrozhdayuschiesya ellipticheskie i giperbolicheskie uravneniya, Nauka, M., 1966 | MR

[12] G. Fichera, “On a unified theory of boundary-value problems for elliptic-parabolic equations of second order”, Boundary Problems in Differential Equations, Univ. Wisconsin Press, Madison, WI, 1960, 97–120 | MR

[13] O. A. Oleinik, E. V. Radkevich, “Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Itogi nauki. Ser. Matematika. Mat. anal. 1969, VINITI, M., 1971, 7–252 | MR | Zbl

[14] V. N. Vragov, “Smeshannaya zadacha dlya odnogo klassa giperbolo-parabolicheskikh uravnenii vtorogo poryadka”, Differents. uravneniya, 12:1 (1976), 24–31 | MR | Zbl

[15] V. N. Vragov, Korrektnye kraevye zadachi dlya neklassicheskikh uravnenii matematicheskoi fiziki, NGU, Novosibirsk, 1983 | MR

[16] S. L. Sobolev, Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR

[17] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[18] H. Triebel, Interpolation Theory, Functional Spaces, Differential Operators, VEB Deutscher Verl. Wiss., Berlin, 1978 | MR

[19] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980 | MR

[20] A. I. Kozhanov, “Nachalno-granichnye zadachi dlya vyrozhdayuschikhsya giperbolicheskikh uravnenii”, Sib. elektron. matem. izv., 18:1 (2021), 43–53 | DOI | MR | Zbl