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Sib. Zh. Ind. Mat., 2012, Volume 15, Number 4, Pages 3–16 (Mi sjim747)  

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

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.

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:1, 1–14

Bibliographic databases:

Document Type: Article
UDC: 517.95
Received: 06.08.2012

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
\Bibitem{AleShe12}
\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://www.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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V R. Brizitskii , Zh. Yu. Saritskaya, I A. Byrganov, “Multiplicative control problems for nonlinear convection-diffusion-reaction equation”, Sib. Electron. Math. Rep., 13 (2016), 352–360  crossref  isi
    2. 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
  • Сибирский журнал индустриальной математики
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