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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 7, Pages 1267–1293
DOI: https://doi.org/10.7868/S0044466916070127
(Mi zvmmf10429)
 

This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (527 kB) Citations (5)
References:
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.
Received: 06.07.2015
Revised: 06.10.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 7, Pages 1238–1263
DOI: https://doi.org/10.1134/S0965542516070125
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
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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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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