Abstract
The main result of our paper is a proof of the uniqueness of the classical solution of a mixed problem for a second-order hyperbolic equation in a normal cylinder.
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V. A. Il'in, “On the solvability of mixed problems for hyperbolic and parabolic equations,” Usp. Matem. Nauk,15, No. 2, 98–154 (1960).
V. A. Il'in and I. A. Shishmarev, “Concerning the equivalence of systems of generalized and classical characteristic functions,” Izv. Akad. Nauk SSSR, Ser. Matem.,24, 757–774 (1960).
M. V. Keldysh, “On the characteristic values and characteristic functions of certain classes of nonself-adjoint equations,” Dokl. Akad. Nauk SSSR,77, No. 1, 11–14 (1951).
C. Miranda, Partial Differential Equations of Elliptic Type, Springer-Verlag, New York (1969).
G. Giraud, “Problémes de valeursá la frontiére relatifs a certaines données discontinues,” Bull. Soc. Math. France,61, 1–54 (1933).
V. I. Smirnov, A Course of Higher Mathematics, Vol. 5, Addison-Wesley, Reading, Mass. (1964).
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Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 437–444, March, 1974.
In conclusion, the author expresses his thanks to V. A. Il'in for his statement of the problem and useful remarks made during the course of my investigation.
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Ponomarev, S.M. Uniqueness of the solution of a second-order hyperbolic equation in a normal cylinder. Mathematical Notes of the Academy of Sciences of the USSR 15, 255–259 (1974). https://doi.org/10.1007/BF01438380
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DOI: https://doi.org/10.1007/BF01438380