References
V. G. Romanov, Some Inverse Problems for the Equations of Hyperbolic Type [in Russian], Nauka, Novosibirsk (1972).
M. M. Lavrent’ev, V. G. Romanov, and S. P. Shishatskiî, Ill-Posed Problems of Mathematical Physics and Analysis [in Russian], Nauka, Moscow (1980).
A. L. Bukhgeîm, Volterra Equations and Inverse Problems [in Russian], Nauka, Novosibirsk (1983).
V. G. Romanov, Inverse Problems of Mathematical Physics [in Russian], Nauka, Moscow (1984).
S. I. Kabanikhin, Projection-Difference Methods for Determining Coefficients of Hyperbolic Equations [in Russian], Nauka, Novosibirsk (1988).
V. G. Romanov, “Uniqueness theorems in inverse problems for some second-order equations”, Dokl. Akad. Nauk SSSR,321, No. 2, 254–257 (1991).
A. L. Bukhgeîm and M. V. Klibanov, “Uniqueness in the large of a class of multidimensional inverse problems”, Dokl. Akad. Nauk SSSR,260, No. 2, 269–272 (1981).
M. A. Kazemi and M. V. Klibanov, “Stability estimates for ill-posed Cauchy problems involving hyperbolic equations and inequalities”, Appl. Anal.,50, No. 1–2, 93–102 (1993).
M. I. Belishev and A. P. Kachalov, “An operator integral in the multidimensional inverse spectral problem”, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI),215 (Differential Geometry. Lie Groups and Mechanics,14), 1994, pp. 9–37.
M. I. Belishev, “An approach to multidimensional inverse problems for the wave equation”, Dokl. Akad. Nauk SSSR,297, No. 3, 524–527 (1987).
V. G. Romanov, “Solvability of inverse problems for hyperbolic equations in a class of functions that are analytic with respect to some of the variables”, Dokl. Akad. Nauk SSSR,304, No. 4, 807–811 (1989).
V. G. Romanov, “On a regularizing algorithm for solving an inverse problem for a hyperbolic equation”, Dokl. Akad. Nauk,346, No. 3, 303–306 (1996).
V. G. Romanov, “On a numerical method for solving a certain inverse problem for a hyperbolic equation”, Sibirsk. Mat. Zh.,37, No. 3, 633–655 (1996).
V. Komornik, Exact Controllability and Stabilization. The Multiplier Method, John Wiley & Sons, New York (1994).
Additional information
The research was financially supported by the Russian Foundation for Basic Research (Grant 96-01-01887) and INTAS—RFBR (Grant 95-0763).
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 39, No. 2, pp. 436–449, March–April, 1998.
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Romanov, V.G. On a stability estimate for a solution to an inverse problem for a hyperbolic equation. Sib Math J 39, 381–393 (1998). https://doi.org/10.1007/BF02677522
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DOI: https://doi.org/10.1007/BF02677522