Optimal multiplicative control for Helmholtz equation
A. S. Savenkova
2008, issue 2, Ñ. 206–217
|Optimal control problem for Helmholtz equation in bounded domain is considered in this paper. Solvability of boundary value problem for Helmholtz equation in Sobolev spaces is studied. The problem of boundary impedance control is stated and investigated. The main result of research is the proof of existence and determination uniqueness conditions for solution to optimal control problem.|
Keywords: optimal control, Helmholtz equation, impedance
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| D. Kolton, R. Kress, Metody integral'nyx uravnenij v teorii rasseyaniya, Mir, M., 1987, 311 s.|
 Liu Changmei, The Helmholtz equation on Lipschitz domains, PhD Thesis Department of Mathematics, University of North Carolina, 1995.
 T. S. Angell, A. Kirsch, Optimization methods in electromagnetic radiation, Springer, 2003.
 A. Habbal, “Nonsmooth Shape Optimization Applied to Linear Acoustics”, SIAM Journal on Optimization, 8:4 (1998), 989–1006.
 Cao Yanzhao, D. Stanescu, “Shape optimization for noise radiation problems”, Computers and Mathematics with Applications, 44 (2002), 1527–1537.
 F. Criado, G. Meladze, N. Odisehlidze, “An optimal control problem for Helmholtz equation with non-local boundary conditions and quadratic functional”, Rev. R. Acad. Cienc. Exactas Fis. Nat. (Esp.), 1:1 (1997), 65–69.
 J. Jahn, A. Kirsch, C. Wagner, “Optimization of rod antennas of mobile phones”, Math. Meth. Oper. Res., 59 (2004), 37–51.
 V. A. Trenogin, Funkcional'nyj analiz, Nauka, M., 1980, 496 s.
 A. D. Ioffe, V. M. Tixomirov, Teoriya e'kstremal'nyx zadach, Nauka, M., 1974, 240 s.
 A. V. Fursikov, Optimal'noe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999, 352 s.