Abstract
Finite difference approximations are proposed for nonlinear optimal control problems for a non-self-adjoint elliptic equation with Dirichlet boundary conditions in a convex domain Ω ⊂ ℝ2 with controls involved in the leading coefficients. The convergence of the approximations with respect to the state, functional, and control is analyzed, and a regularization of the approximations is proposed.
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Original Russian Text © F.V. Lubyshev, A.R. Manapova, 2013, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2013, Vol. 53, No. 1, pp. 20–46.
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Lubyshev, F.V., Manapova, A.R. Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives. Comput. Math. and Math. Phys. 53, 8–33 (2013). https://doi.org/10.1134/S0965542513010053
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DOI: https://doi.org/10.1134/S0965542513010053