Geodesic
One the masking problem for the two-dimensional Helmholtz equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 378-392

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Control problems for 2-D Helmholtz equation in a bounded domain with mixed boundary conditions are considered. The boundary impedance entering into impedance boundary condition for the field plays the role of control. The solvability of both the direct problem and the control problem is proved. The uniqueness and stability of optimal solutions with respect to small perturbations of both the cost functional and a given function are established.
Keywords: Helmholtz equation, mixed boundary value problem, control problem, boundary control, solvability, stability estimates.
Mots-clés : impedance 
@article{SEMR_2013_10_a50,
     author = {A. V. Lobanov and R. V. Zubrev},
     title = {One the masking problem for the two-dimensional {Helmholtz} equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {378--392},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a50/}
}
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A. V. Lobanov; R. V. Zubrev. One the masking problem for the two-dimensional Helmholtz equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 378-392. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a50/