On reducing the inverse boundary value problem to the synthesis of two ill-posed problems and their solution
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 2, pp. 219-232.

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This paper concerns the solution of the inverse boundary value problem for the equation of thermal conductivity and the estimation of the approximate solution error. The Fourier transform with respect to time, which allows one to obtain an error estimate, is not applicable to the problem to be solved. Therefore, in the equation of thermal conductivity, the variable was replaced, which led to the synthesis of problems and allowed obtaining an estimate.
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V. P. Tanana. On reducing the inverse boundary value problem to the synthesis of two ill-posed problems and their solution. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 2, pp. 219-232. http://geodesic.mathdoc.fr/item/SJVM_2020_23_2_a8/

[1] O. M. Alifanov, E. A. Artyukhin, S. V. Rumyantsev, Ekstremal'nye metody resheniya nekorrektnykh zadach, Nauka, M., 1988 | MR

[2] V. P. Tanana, “Ob optimal'nosti po poryadku metoda proektsionnoi regulyarizatsii pri reshenii obratnykh zadach”, Sib. zhurn. industr. matem., 7:2 (2004), 117–132 | MR | Zbl

[3] Tanana V.P., “An order-optimal method for solving an inverse problem for a parabolic equation”, Num. Anal. Appl., 3:4 (2010), 367–380 | DOI | MR | MR | Zbl

[4] V. P. Tanana, A. I. Sidikova, “O garantirovannoi otsenke tochnosti priblizhennogo resheniya odnoi obratnoi zadachi teplovoi diagnostiki”, Tr. IMM UrO RAN, 16, no. 2, 2010, 1–15

[5] A. N. Tikhonov, “O regulyarizatsii nekorrektno postavlennykh zadach”, DAN SSSR, 153:1 (1963), 9–52 | MR

[6] M. M. Lavrent'ev, “O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki”, SO AN SSSR, Novosibirsk, 1962

[7] V. K. Ivanov, “O nekorrektno postavlennykh zadachakh”, Mat. sbornik, 61:2 (1963), 211–213

[8] D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind”, J. Assoc. Comput. Mach., 9:1 (1962), 84–97 | DOI | MR | Zbl

[9] V. K. Ivanov, “O priblizhennom reshenii operatornykh uravnenii”, Zhurn. vychisl. matem. i mat. fiziki, 6:6 (1966), 1089–1094

[10] Morozov V.A., “Regularization of incorrectly posed problems and the choice of regularization parameter”, U.S.S.R. Comput. Math. Math. Phys., 6:1 (1966), 242–251 | DOI | MR | Zbl

[11] Ivanov V.K., Korolyuk T.I., “Error estimates for solutions of incorrectly posed linear problems”, U.S.S.R. Comput. Math. Math. Phys., 9:1 (1969), 35–49 | DOI | MR | Zbl

[12] V. P. Tanana, “Ob optimal'nosti metodov resheniya nelineinykh neustoichivykh zadach”, DAN SSSR, 220:5 (1975), 1035–1037 | Zbl

[13] V. K. Ivanov, V. V. Vasin, V. P. Tanana, Theory of Linear Ill-Posed Problems and its Applications, VSP, Netherland, 2002 | MR | Zbl

[14] V. P. Tanana, T. N. Rudakova, “The optimum of the M.M. Lavrent'ev method”, J. of Inverse and Ill-Posed Problems, 18 (2011), 935–944 | DOI | MR

[15] V. P. Tanana, A. I. Sidikova, Optimal Methods for Ill-Posed Problems with Applications to Heat Conduction, De Gruyter, 2018 | MR | Zbl

[16] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsional'nogo analiza, Nauka, M., 1989