V. P. Tanana, “On reducing the inverse boundary value problem to the synthesis of two ill-posed problems and their solution”, Sib. Zh. Vychisl. Mat., 23:2 (2020), 219–232; Num. Anal. Appl., 13:2 (2020), 180

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2020, Volume 23, Number 2, Pages 219–232
DOI: https://doi.org/10.15372/SJNM20200208 (Mi sjvm744)

This article is cited in 9 scientific papers (total in 9 papers)

On reducing the inverse boundary value problem to the synthesis of two ill-posed problems and their solution

V. P. Tanana^ab

^a South Ural State University, pr. Lenina 76, Chelyabinsk, 454080 Russia
^b Chelyabinsk State University, ul. Brat’ev Kashirinykh 129, Chelyabinsk, 454001 Russia

Full-text PDF (579 kB) Citations (9)

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DOI: https://doi.org/10.15372/SJNM20200208

Abstract: 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.

Key words: error estimation, modulus of continuity, Fourier transform, ill-posed problem.

Received: 18.06.2018
Revised: 21.03.2019
Accepted: 19.12.2019

English version:
Numerical Analysis and Applications, 2020, Volume 13, Issue 2, Pages 180–192
DOI: https://doi.org/10.1134/S1995423920020081

Bibliographic databases:

Document Type: Article

UDC: 517.948

Language: Russian

Citation: V. P. Tanana, “On reducing the inverse boundary value problem to the synthesis of two ill-posed problems and their solution”, Sib. Zh. Vychisl. Mat., 23:2 (2020), 219–232; Num. Anal. Appl., 13:2 (2020), 180–192

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sjvm744

https://www.mathnet.ru/eng/sjvm/v23/i2/p219

This publication is cited in the following 9 articles:

V. P. Tanana, B. A. Markov, “On the error in determining the protective layer boundary in the inverse heat problem”, J. Appl. Industr. Math., 17:4 (2023), 859–873
A. I. Sidikova, H. K. Al-Mahdawi, PROCEEDING OF THE 1ST INTERNATIONAL CONFERENCE ON ADVANCED RESEARCH IN PURE AND APPLIED SCIENCE (ICARPAS2021): Third Annual Conference of Al-Muthanna University/College of Science, 2398, PROCEEDING OF THE 1ST INTERNATIONAL CONFERENCE ON ADVANCED RESEARCH IN PURE AND APPLIED SCIENCE (ICARPAS2021): Third Annual Conference of Al-Muthanna University/College of Science, 2022, 060050
Hassan K. Ibrahim Al-Mahdawi, Mostafa Abotaleb, Hussein Alkattan, Al-Mahdawi Zena Tareq, Amr Badr, Ammar Kadi, “Multigrid Method for Solving Inverse Problems for Heat Equation”, Mathematics, 10:15 (2022), 2802
H.K. Al-Mahdawi, A. I Sidikova, Hussein Alkattan, Mostafa Abotaleb, Ammar Kadi, El-Sayed M El-kenawy, “Parallel multigrid method for solving inverse problems”, MethodsX, 9 (2022), 101887
Roman S. Tikhonov, Nikolay P. Starostin, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 020006
V. P. Tanana, B. A. Markov, A. I. Sidikova, “Solution of the inverse boundary value problem of heat transfer for an inhomogeneous ball”, Num. Anal. Appl., 14:3 (2021), 269–286
A. I. Sidikova, A. S. Sushkov, “Chislennoe reshenie obratnoi granichnoi zadachi teploobmena dlya neodnorodnogo sterzhnya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:2 (2021), 253–264
A. Zamyshlyaeva, A. Lut, “Inverse problem for the Sobolev type equation of higher order”, Mathematics, 9:14 (2021), 1647
V P Tanana, M E Korzhova, B A Markov, “On the protective layer boundary determining error in the thermal conductivity inverse problem”, J. Phys.: Conf. Ser., 2099:1 (2021), 012048

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Sibirskii Zhurnal Vychislitel'noi Matematiki

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