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Sibirskii Zhurnal Industrial'noi Matematiki, 2012, Volume 15, Number 4, Pages 3–16 (Mi sjim747)  
This article is cited in 4 scientific papers (total in 4 papers)

On the stability of solutions to coefficient inverse extreme problems for the stationary convection-diffusion equation

G. V. Alekseevab, M. A. Shepelovac

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia
b Vladivostok State University of Economics and Service, Vladivostok, Russia
c Far Eastern Federal University, Vladivostok, Russia
Full-text PDF (298 kB) Citations (4)
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Abstract: We study the coefficient inverse problem for the extreme stationary convection-diffusion, considered in a bounded domain with mixed boundary conditions on the boundary. The role of control is played by the velocity vector of the medium and the functions involved in the boundary conditions for the temperature. The solvability of extremal problems is proved for arbitrary weak lower semicontinuous quality functional as well as for specific quality functionals. On the basis of the analysis of the optimality system, we establish sufficient conditions on the initial data that guarantee the uniqueness and stability of optimal solutions under small perturbations of the quality functional as well as of one of the functions outside the initial boundary value problem.
Keywords: convection-diffusion equation, temperature, velocity vector, multiplicative control, coefficient inverse problems, existence, uniqueness, stability.
Received: 06.08.2012
English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 1, Pages 1–14
DOI: https://doi.org/10.1134/S1990478913010018
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: G. V. Alekseev, M. A. Shepelov, “On the stability of solutions to coefficient inverse extreme problems for the stationary convection-diffusion equation”, Sib. Zh. Ind. Mat., 15:4 (2012), 3–16; J. Appl. Industr. Math., 7:1 (2013), 1–14
Citation in format AMSBIB
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\by G.~V.~Alekseev, M.~A.~Shepelov
\paper On the stability of solutions to coefficient inverse extreme problems for the stationary convection-diffusion equation
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 4
\pages 3--16
\mathnet{http://mi.mathnet.ru/sjim747}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3112354}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 1
\pages 1--14
\crossref{https://doi.org/10.1134/S1990478913010018}
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  • https://www.mathnet.ru/eng/sjim747
  • https://www.mathnet.ru/eng/sjim/v15/i4/p3
    • This publication is cited in the following 4 articles:
    1. Vitaly A. Likhoshvai, Vladimir P. Golubyatnikov, Tamara M. Khlebodarova, “Limit cycles in models of circular gene networks regulated by negative feedback loops”, BMC Bioinformatics, 21:S11 (2020)  crossref
    2. Brizitskii V R., Saritskaya Zh.Y., “Optimization Analysis of the Inverse Coefficient Problem For the Nonlinear Convection-Diffusion-Reaction Equation”, J. Inverse Ill-Posed Probl., 26:6 (2018), 821–833  crossref  mathscinet  zmath  isi  scopus
    3. R. V. Brizitskii, Zh. Yu. Saritskaya, A. I. Byrganov, “Multiplicative control problems for nonlinear convection-diffusion-reaction equation”, Sib. Electron. Math. Rep., 13 (2016), 352–360  crossref  isi
    4. O. V. Soboleva, R. V. Brizitskii, “Numerical study of the inverse problem for the diffusion-reaction equation using optimization method”, International Conference on Mechanical Engineering, Automation and Control Systems 2015 (MEACS 2015), IOP Conference Series-Materials Science and Engineering, 124, IOP Publishing Ltd, 2016, UNSP 012096  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал индустриальной математики
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