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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2013, Volume 10, Pages 378–392 (Mi semr418)  
Differentical equations, dynamical systems and optimal control

One the masking problem for the two-dimensional Helmholtz equation

A. V. Lobanova, R. V. Zubrevb

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok
b Far Eastern State Technical Fisheries University
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Abstract: 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, impedance, control problem, boundary control, solvability, stability estimates.
Received February 1, 2013, published April 14, 2013
Document Type: Article
UDC: 517.95
MSC: 35Q93
Language: Russian
Citation: A. V. Lobanov, R. V. Zubrev, “One the masking problem for the two-dimensional Helmholtz equation”, Sib. Èlektron. Mat. Izv., 10 (2013), 378–392
Citation in format AMSBIB
\Bibitem{LobZub13}
\by A.~V.~Lobanov, R.~V.~Zubrev
\paper One the masking problem for the two-dimensional Helmholtz equation
\jour Sib. \`Elektron. Mat. Izv.
\yr 2013
\vol 10
\pages 378--392
\mathnet{http://mi.mathnet.ru/semr418}
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