Abstract:
This paper is concerned with investigating and solving the mixed initial boundary value problem for the heat conduction equation. The statement of the problem includes the three intervals: the first one (from 0→T1) describes heating the combustion chamber, the second (from T1→T2) — cooling the chamber and a slower cooling of its wall. Finally, the third interval describes natural cooling of the chamber wall when the chamber has the temperature coinciding with that of environment. The validity of the application of the Fourier transform with respect to this problem has been proved. This made possible to transform the governing equation to the ordinary differential equation. By using the resulting equation, the inverse boundary value problem for the heat conduction equation by applying the nonlinear method of projection regularization was solved and the error of approximate solution was obtained.
Citation:
A. I. Sidikova, “The study of an inverse boundary problem for the heat conduction equation”, Sib. Zh. Vychisl. Mat., 22:1 (2019), 81–98; Num. Anal. Appl., 12:1 (2019), 70–86
\Bibitem{Sid19}
\by A.~I.~Sidikova
\paper The study of an inverse boundary problem for the heat conduction equation
\jour Sib. Zh. Vychisl. Mat.
\yr 2019
\vol 22
\issue 1
\pages 81--98
\mathnet{http://mi.mathnet.ru/sjvm702}
\crossref{https://doi.org/10.15372/SJNM20190106}
\elib{https://elibrary.ru/item.asp?id=37062942}
\transl
\jour Num. Anal. Appl.
\yr 2019
\vol 12
\issue 1
\pages 70--86
\crossref{https://doi.org/10.1134/S1995423919010063}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000463783600006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85063999194}
Linking options:
https://www.mathnet.ru/eng/sjvm702
https://www.mathnet.ru/eng/sjvm/v22/i1/p81
This publication is cited in the following 4 articles:
Bashar Talib Al-Nuaimi, H.K. Al-Mahdawi, Zainalabideen Albadran, Hussein Alkattan, Mostafa Abotaleb, El-Sayed M. El-kenawy, “Solving of the Inverse Boundary Value Problem for the Heat Conduction Equation in Two Intervals of Time”, Algorithms, 16:1 (2023), 33
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
I. V. Boykov, V. A. Ryazantsev, “An approximate method for solving the inverse coefficient problem
for the heat equation”, J. Appl. Industr. Math., 15:2 (2021), 175–189
Ch. Zhao, Zh. Zhang, “Dynamic error correction of filament thermocouples with different structures of junction based on inverse filtering method”, Micromachines, 11:1 (2020), 44
Citation in format AMSBIB
Contact us: