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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 8, Pages 1378–1399 (Mi zvmmf9703)  
This article is cited in 6 scientific papers (total in 6 papers)

Finite difference approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions

F. V. Lubyshev

Bashkortostan State University, ul. Zaki Validi 32, Ufa, 450074 Russia
Full-text PDF (1960 kB) Citations (6)
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Abstract: Mathematical formulation of nonlinear optimal control problems for semilinear elliptic equations with discontinuous coefficients and discontinuous solutions 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, finite difference solution method, regularization.
Received: 10.10.2011
Revised: 22.02.2012
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 8, Pages 1094–1114
DOI: https://doi.org/10.1134/S0965542512080088
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: F. V. Lubyshev, “Finite difference approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions”, Zh. Vychisl. Mat. Mat. Fiz., 52:8 (2012), 1378–1399; Comput. Math. Math. Phys., 52:8 (2012), 1094–1114
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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