Literature Cited
M. J. Hadamard, On problems in partial derivatives, and their physical significance [in French], Bull. Princeton Univ., 13, 82–88 (1902).
M. J. Hadamard, Cauchy's Problem [in French], Hermann, Paris (1932).
A. N. Tikhonov, On the stability of inverse problems, DAN SSSR,39, 5, 195–198 (1944).
N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications, J. Wiley, New York (1950).
F. John, Differential Equations with Approximate and Improper Data, Lectures, New York Univ. Press (1955).
F. John, A note on improper problems, Comm. Pure Appl. Math.,8, 1, 13–18 (1955).
C. Pucci, Sul problemi di Cauchy non ben posti, Atti delle Acad. Naz. Lincei,8, 18, 411–418 (1955).
M. M. Lavrent'ev, On Cauchy's problem for the Laplace equation, DAN SSSR,102, 2, 205–206 (1955).
R. L. Dobrushin, General formulation of Shannon's basic theorems in information theory, Uspekhi matem. nauk,14, 6, 3–104 (1959).
M. M. Lavrent'ev, Some Incorrect Problems of Mathematical Physics [in Russian], Novosibirsk (1962).
V. K. Ivanov, On incorrectly posed problems, Matem. sb.,61, 2, 211–222 (1963).
A. N. Tikhonov, On the regularization of incorrectly posed problems, DAN SSSR,153, 1, 49–52 (1963).
V. N. Sudakov and L. A. Khalfin, Statistical approach to the correctness of problems of mathematical physics, DAN SSSR,157, 5, 1058–1060 (1964).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 7, No. 3, pp. 559–576, May–June, 1966.
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Lavrent'ev, M.M., Vasil'ev, V.G. The posing of certain improper problems of mathematical physics. Sib Math J 7, 450–463 (1966). https://doi.org/10.1007/BF00966243
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DOI: https://doi.org/10.1007/BF00966243