Geodesic
On certain problems of optimal control and their approximations for some non-self-adjoint elliptic equations of the convection-diffusion type
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical analysis, Tome 143 (2017), pp. 3-23.

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In this paper, we construct finite-difference approximations of optimal-control problems involving bob-self-adjoint convection-diffusion elliptic equations with discontinuous coefficients and states and examine the convergence of these approximations. Control functions in these problems are the coefficients of the convective-transfer operator in the equation of state and its right-hand side. We study the well-posedness of problems considered. For finite-difference approximations, we obtain estimates of the exactness by the state and the convergence rate by the functional and prove the weak convergence by the control. In addition, we regularize approximations in the Tikhonov sense.
Keywords: optimal-control problem, semilinear elliptic equation, non-self-adjoint operator, operator of diffusive and convective transfer, finite-difference methods. 
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     author = {F. V. Lubyshev and A. R. Manapova},
     title = {On certain problems of optimal control and their approximations for some non-self-adjoint elliptic equations of the convection-diffusion type},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--23},
     publisher = {mathdoc},
     volume = {143},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_143_a0/}
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F. V. Lubyshev; A. R. Manapova. On certain problems of optimal control and their approximations for some non-self-adjoint elliptic equations of the convection-diffusion type. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical analysis, Tome 143 (2017), pp. 3-23. http://geodesic.mathdoc.fr/item/INTO_2017_143_a0/