This article is cited in 4 scientific papers (total in 4 papers)
Approximate solution of an inverse boundary value problem for a system of differential equations of parabolic type and estimation of the error of this solution
Abstract:
We study the problem of finding a boundary condition in the heat equation for a hollow ball made of a composite material consisting of two homogeneous components. The Dirichlet condition is considered as boundary conditions inside the ball at r=r0. In the inverse problem, the temperature inside the ball is assumed to be unknown on an infinite time interval. For finding it, the temperature of the heat flux at the media interface for r=r1 is measured. We analyze the direct problem, which allows us to give a strict formulation of the inverse problem and determine the functional spaces in which it is natural to solve the inverse problem. Estimating the error of the approximate solution presents a major difficulty, which is dealt with in this paper by the method of projection regularization. Using this method, we find order-exact estimates.
Keywords:
error estimation, modulus of continuity, Fourier transform, ill-posed problem.
Citation:
V. P. Tanana, A. I. Sidikova, “Approximate solution of an inverse boundary value problem for a system of differential equations of parabolic type and estimation of the error of this solution”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 3, 2019, 247–264
\Bibitem{TanSid19}
\by V.~P.~Tanana, A.~I.~Sidikova
\paper Approximate solution of an inverse boundary value problem for a system of differential equations of parabolic type and estimation of the error of this solution
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 3
\pages 247--264
\mathnet{http://mi.mathnet.ru/timm1662}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-3-247-264}
\elib{https://elibrary.ru/item.asp?id=39323552}
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https://www.mathnet.ru/eng/timm/v25/i3/p247
This publication is cited in the following 4 articles:
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
I. V. Boykov, V. A. Ryazantsev, “On the problem of recovering boundary conditions in the third boundary value problem for parabolic equation”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2021, no. 2, 3–13
V. P. Tanana, “Polnota sistemy sobstvennykh funktsii zadachi Shturma–Liuvillya s osobennostyu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:1 (2020), 59–63
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
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