Geodesic
On estimating the errors of approximate solution methods for an inverse problem
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 2, pp. 135-148 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study an inverse boundary problem for the heat equation for an inhomogeneous rod composed of two materials. We consider three different situations of temperature measurements inside the rod, from which we must reconstruct one of the boundary values of the problem. Similar problems arise in the test benching of rocket engines, and their solutions are required to be very precise. We solve the problems by the projection regularization method, and for their solutions we obtain estimates that are precise up to the order of magnitude.
Keywords: inverse heat conduction problems, projection regularization method, estimates precise up to the order of magnitude.
Mots-clés : Fourier transform 
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S. M. Serebryanskiǐ. On estimating the errors of approximate solution methods for an inverse problem. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 2, pp. 135-148. http://geodesic.mathdoc.fr/item/SJIM_2010_13_2_a12/

[1] Alifanov O. M., Obratnye zadachi teploobmena, Mashinostroenie, M., 1988

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

[3] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972

[4] Tanana V. P., Metody resheniya operatornykh uravnenii, Nauka, M., 1981 | MR