Geodesic
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
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 54-69

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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, difference method.
Mots-clés : convective and diffusion transfer 
@article{SVMO_2016_18_1_a6,
     author = {F. V. Lubyshev and A. R. Manapova and M. \`E. Fairuzov},
     title = {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},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {54--69},
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     volume = {18},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a6/}
}
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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. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 1, pp. 54-69. http://geodesic.mathdoc.fr/item/SVMO_2016_18_1_a6/