zbMATH — the first resource for mathematics

Difference approximations of optimization problems for semilinear elliptic equationsin a convex domain with controls in the coefficients multiplying the highest derivatives. (Russian, English) Zbl 1274.49007
Zh. Vychisl. Mat. Mat. Fiz. 53, No. 1, 20-46 (2013); translation in Comput. Math. Math. Phys. 53, No. 1, 8-33 (2013).
Summary: 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 \(\Omega \in \mathbb R^2\) 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.

49J20 Existence theories for optimal control problems involving partial differential equations
35J61 Semilinear elliptic equations
Full Text: DOI Link