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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 3, Pages 98–113 (Mi timm1088)  

This article is cited in 2 scientific papers (total in 2 papers)

Direct and inverse boundary value problems for models of stationary reaction-convection-diffusion

A. I. Korotkiiab, Yu. V. Starodubtsevaa

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University

Abstract: Direct and inverse boundary value problems for models of stationary reaction-convection-diffusion are investigated. The direct problem consists in finding a solution of the corresponding boundary value problem for given data on the boundary of the domain of the independent variable. The peculiarity of the direct problem consists in the inhomogeneity and irregularity of mixed boundary data. Solvability and stability conditions are specified for the direct problem. The inverse boundary value problem consists in finding some traces of the solution of the corresponding boundary value problem for given standard and additional data on a certain part of the boundary of the domain of the independent variable. The peculiarity of the inverse problem consists in the ill-posedness of this problem. Regularizing methods and solution algorithms are developed for the inverse problem.

Keywords: direct problem, mixed boundary condition, weak solution, stability, inverse problem, regularization, iterative methods.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 291, suppl. 1, 96–112

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 21.03.2014

Citation: A. I. Korotkii, Yu. V. Starodubtseva, “Direct and inverse boundary value problems for models of stationary reaction-convection-diffusion”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 98–113; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 96–112

Citation in format AMSBIB
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\paper Direct and inverse boundary value problems for models of stationary reaction-convection-diffusion
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 3
\pages 98--113
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 291
\issue , suppl. 1
\pages 96--112
\crossref{https://doi.org/10.1134/S0081543815090072}
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    This publication is cited in the following articles:
    1. Zh. Yu. Saritskaya, “Stability of Inverse Coefficient Problems' Solutions For Semilinear Equations”, Proceedings of the International Conference on Days on Diffraction, DD 2016, eds. O. Motygin, A. Kiselev, P. Kapitanova, L. Goray, A. Kazakov, A. Kirpichnikova, IEEE, 2016, 361–366  crossref  isi  scopus
    2. A. I. Korotkii, A. L. Litvinenko, “Razreshimost odnoi smeshannoi kraevoi zadachi dlya statsionarnoi modeli reaktsii-konvektsii-diffuzii”, Vypusk posvyaschen 70-letnemu yubileyu Aleksandra Georgievicha Chentsova, Tr. IMM UrO RAN, 24, no. 1, 2018, 106–120  mathnet  crossref  elib
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