Stochastic regularization of ill-posed problems of heat transfer
DOI:
https://doi.org/10.15407/dopovidi2014.06.080Keywords:
heat transfer, stochastic regularizationAbstract
The stochastic approximation of the parabolic equation of heat conduction and its subsequent averaging over realizations of random parameters leads to an equation of the hyperbolic type for the average values of transfer functions. On a basis of this equation, the statements of inverse problems concerning the restoration of boundary conditions are well-posed.
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Tikhonov A. N. On ill-posed problems. In: Computational methods and programming. Moscow: Izd-vo Mosk. un-ta, 1967: 3–33 (in Russian).
Turchin V. F., Kozlov V. P.,Malkevich M. S. Usp. fiz. nauk, 1970, 102, No. 3: 345–386 (in Russian).
Matsevity Yu. M., Lyshpenko S. F. Identification of thermophysical properties of solids.Kyiv: Nauk. dumka, 1990 (in Russian).
Kalman R., Biysi R. Tr. amerik. ob-va inzh.-mekh. Ser. D., 1961, 83, No. 1: 123–141 (in Russian).
Klibanov M. V. Dokl. AN USSR, 1985, 280, No. 3: 533–536 (in Russian).
Lavrentyev M. M., Romanov V. G., Shyshatskiy S. P. Ill-posed problems of mathematical physics and analysis. Moscow: Nauka, 1980 (in Russian).
Derevich I. V., Zaychik L. I. Prikl. mekh. i mat., 1990, 4, No. 5: 767–774 (in Russian).
Krivoshey F. A. Zhurn. vychislit. matematiki i mat. fiziki, 1993, 33, No. 7: 1103–1109 (in Russian).
Klyatskin V. I. Stochastic equations and waves in randomly inhomogeneous media. Moscow: Nauka, 1980 (in Russian).
Novikov E. A. Zhurn.eksperim. i teoret. fiziki, 1964, 47, No. 6: 1919–1926 (in Russian).
Lavrentyev M. M. On ill-posed problems of mathematical physics. Moscow: AS USSR, 1962 (in Russian).
Lattes R., Lionis Zh. L. Method of quasi-inversion and its applications. Moscow: Mir, 1970 (in Russian).
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