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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 7, Pages 1267–1293 (Mi zvmmf10429)  

This article is cited in 4 scientific papers (total in 4 papers)

Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and states and with controls in the coefficients multiplying the highest derivatives

F. V. Lubyshev, M. E. Fairuzov

Bashkir State University, ul. Zaki Validi 32, Ufa, Bashkortostan, 450074, Russia

Abstract: Mathematical formulations of nonlinear optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with controls in the coefficients multiplying the highest derivatives are studied. Finite difference approximations of optimization problems are constructed, and the approximation error is estimated with respect to the state and the cost functional. Weak convergence of the approximations with respect to the control is proved. The approximations are regularized in the sense of Tikhonov.

Key words: optimal control problem, semilinear elliptic equations, difference solution method, regularization method.

DOI: https://doi.org/10.7868/S0044466916070127

Full text: PDF file (527 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:7, 1238–1263

Bibliographic databases:

UDC: 519.626
Received: 06.07.2015
Revised: 06.10.2015

Citation: F. V. Lubyshev, M. E. Fairuzov, “Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and states and with controls in the coefficients multiplying the highest derivatives”, Zh. Vychisl. Mat. Mat. Fiz., 56:7 (2016), 1267–1293; Comput. Math. Math. Phys., 56:7 (2016), 1238–1263

Citation in format AMSBIB
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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. F. V. Lubyshev, A. R. Manapova, M. E. Fairuzov, “Approksimatsiya zadach optimalnogo upravleniya dlya polulineinykh ellipticheskikh uravnenii konvektsii-diffuzii s razryvnymi koeffitsientami i sostoyaniyami, s upravleniyami v koeffitsientakh operatorov diffuzionnogo i konvektivnogo perenosa”, Zhurnal SVMO, 18:1 (2016), 54–69  mathnet  elib
    2. F. V. Lubyshev, M. E. Fairuzov, “Consistent convergence rate estimates in the grid $W_{2,0}^2(\omega)$ norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from $W_{2,0}^m(\Omega)$, $3<m\leqslant4$”, Comput. Math. Math. Phys., 57:9 (2017), 1427–1452  mathnet  crossref  crossref  isi  elib  elib
    3. F. V. Lubyshev, M. E. Fairuzov, A. R. Manapova, “Tochnost raznostnykh skhem dlya nelineinykh ellipticheskikh uravnenii s neogranichennoi nelineinostyu”, Zhurnal SVMO, 19:3 (2017), 41–52  mathnet  crossref  elib
    4. F. V. Lubyshev, A. R. Manapova, “Approksimatsiya zadach optimalnogo upravleniya koeffitsientami ellipticheskikh uravnenii konvektsii-diffuzii s usloviyami sopryazheniya tipa neidealnogo kontakta”, Zhurnal SVMO, 21:2 (2019), 187–214  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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