Geodesic
Control of boundary impedance in two-dimensional material-body cloaking by the wave flow method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 2044-2061

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Control problems are considered for a two-dimensional electromagnetic field model describing electromagnetic wave scattering in a unbounded homogeneous medium containing an anisotropic permeable inclusion with a partially covered (cloaked) boundary. The control is a function involved in the impedance boundary condition on the covered part of the boundary. The solvability of the original mixed transmission problem for the two-dimensional Helmholtz equation and of the control problems is proved. Optimality systems describing necessary extremum conditions are derived. The uniqueness and stability of optimal solutions with respect to certain perturbations of the cost functional and the incident wave are established. 
@article{ZVMMF_2013_53_12_a8,
     author = {G. V. Alekseev},
     title = {Control of boundary impedance in two-dimensional material-body cloaking by the wave flow method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2044--2061},
     publisher = {mathdoc},
     volume = {53},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a8/}
}
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G. V. Alekseev. Control of boundary impedance in two-dimensional material-body cloaking by the wave flow method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 2044-2061. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a8/