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 Zhurnal SVMO, 2016, Volume 18, Number 1, Pages 54–69 (Mi svmo579)

Mathematics

Approximation of optimal control problems for semi-linear elliptic convection-diffusion equations with discontinuous coefficients and states, with controls involved in the coefficients of diffusion and convective transfer

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

Bashkir State University, Ufa

Abstract: In this paper we study main problems of approximation of nonlinear optimal control problems described by elliptic convection-diffusion equations with discontinuous coefficients and solutions, with controls involved in the coefficients of diffusion and convective transfer. Issues of discrete optimization problems construction, convergence of the approximations with respect to state, functional and control, and regularization of approximations are considered.

Keywords: the problem of optimal control, semi-linear elliptic equations, convective and diffusion transfer, difference method

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÌÊ-4147.2015.1

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UDC: 519.626

Citation: F. V. Lubyshev, A. R. Manapova, M. È. Fairuzov, “Approximation of optimal control problems for semi-linear elliptic convection-diffusion equations with discontinuous coefficients and states, with controls involved in the coefficients of diffusion and convective transfer”, Zhurnal SVMO, 18:1 (2016), 54–69

Citation in format AMSBIB
\Bibitem{LubManFai16} \by F.~V.~Lubyshev, A.~R.~Manapova, M.~\E.~Fairuzov \paper Approximation of optimal control problems for semi-linear elliptic convection-diffusion equations with discontinuous coefficients and states, with controls involved in the coefficients of diffusion and convective transfer \jour Zhurnal SVMO \yr 2016 \vol 18 \issue 1 \pages 54--69 \mathnet{http://mi.mathnet.ru/svmo579} \elib{https://elibrary.ru/item.asp?id=26322420} `