Abstract
The stability of the solutions of a group of problems regarding the construction of an underground contour on the basis of the distribution of filtration pressure is considered for bounded and unbounded depths of the water-permeable layer and also for the case of an inclined water-resistant boundary.
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E. G. Tumashev and M. T. Nuzhin, Inverse Boundary-Value Problems and Their Applications [in Russian], Izd. Kazansk. Univ., Kazan' (1965).
R. B. Salimov and Yu. M. Molokovich, “Inverse problem of hydroaeromechanics regarding a change of profiles,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4 (1963).
Hoang Tin Zung, “Stability of the inverse boundary-value problem of analytical functions,” Izv. Akad. Nauk BelorusSSR, Ser. Fiz.-Mat. Nauk, No. 4 (1967).
G. M. Goluzin, Geometrical Theory of the Functions ofa Complex Variable [in Russian], Nauka, Moscow (1966).
Koang Tin Zung, “Stability of the inverse boundary-value problem in the case of a many-sheeted solution and certain generalizations,” Izv. Akad. Nauk BelorusSSR, Ser. Fiz.- Mat. Nauk, No. 4 (1968).
L. N. Kuznetsova, “Uniqueness and stability of the solutions of inverse boundary-value problems,” in: Transactions of a Seminar on Boundary-Value Problems [in Russian], No. 11, Izd. Kazansk. Univ., Kazan' (1974).
L. N. Kuznetsova, Stability of the Solutions of Inverse Boundary-Value Problems in Space Ck [in Russian], Izd. Kazansk. Univ., Kazan', Dep. No. 718-75 (1975).
M. T. Nuzhin and N. B. Il'inskii, “Methods of constructing the underground contour of hydrotechnical installations,” in: Inverse Boundary-Value Problems of Filtration Theory [in Russian], Izd. Kazansk. Univ., Kazan' (1963).
F. D. Gakhov, Boundary-Value Problems [in Russian], Fizmatgiz, Moscow (1963).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1972).
N. B. Salimov, “Inverse problem with an inclined water barrier,” in: Transactions of a Seminar on Boundary-Value Problems [in Russian], No. 3, Izd. Kazansk. Univ., Kazan' (1966).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 54–63, March–April, 1977.
In conclusion, the author wishes to thank L. A. Aksent'ev for constant interest in the work and valuable comments.
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Elizarov, A.M. Stability of the solutions of inverse mixed boundary-value problems such as those encountered in filtration theory. Fluid Dyn 12, 210–217 (1977). https://doi.org/10.1007/BF01050690
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DOI: https://doi.org/10.1007/BF01050690