Abstract
We consider control problems for the 2-D Helmholtz equation in an unbounded domain with partially coated boundary. Dirichlet boundary condition is given on one part of the boundary and the impedance boundary condition is imposed on another its part. The role of control in control problem under study is played by boundary impedance. Quadratic tracking–type functionals for the field play the role of cost functionals. Solvability of control problems is proved. The uniqueness and stability of optimal solutions with respect to certain perturbations of both cost functional and incident field are established.
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