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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 11, Pages 1767–1792
DOI: https://doi.org/10.7868/S0044466914110088 (Mi zvmmf10112) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching boundary conditions

F. V. Lubyshev, A. R. Manapova, M. E. Fairuzov

Bashkir State University, ul. Zaki Validi 32, Ufa, 450074, Bashkortostan, Russia
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DOI: https://doi.org/10.7868/S0044466914110088
Abstract: Mathematical formulations of nonlinear optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching conditions are examined. 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 using Tikhonov regularization.
Key words: optimal control problem, semilinear elliptic equations, difference solution method, regularization method.
Received: 25.11.2013
Revised: 23.03.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 11, Pages 1700–1724
DOI: https://doi.org/10.1134/S0965542514110086
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: F. V. Lubyshev, A. R. Manapova, M. E. Fairuzov, “Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with control in matching boundary conditions”, Zh. Vychisl. Mat. Mat. Fiz., 54:11 (2014), 1767–1792; Comput. Math. Math. Phys., 54:11 (2014), 1700–1724
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
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