Geodesic
Optimal multiplicative control for Helmholtz equation
Dalʹnevostočnyj matematičeskij žurnal, Tome 8 (2008) no. 2, pp. 206-217.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DVMG_2008_8_2_a5,
     author = {A. S. Savenkova},
     title = {Optimal multiplicative control for {Helmholtz} equation},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {206--217},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2008_8_2_a5/}
}
TY  - JOUR
AU  - A. S. Savenkova
TI  - Optimal multiplicative control for Helmholtz equation
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2008
SP  - 206
EP  - 217
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2008_8_2_a5/
LA  - ru
ID  - DVMG_2008_8_2_a5
ER  - 
%0 Journal Article
%A A. S. Savenkova
%T Optimal multiplicative control for Helmholtz equation
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2008
%P 206-217
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2008_8_2_a5/
%G ru
%F DVMG_2008_8_2_a5
A. S. Savenkova. Optimal multiplicative control for Helmholtz equation. Dalʹnevostočnyj matematičeskij žurnal, Tome 8 (2008) no. 2, pp. 206-217. http://geodesic.mathdoc.fr/item/DVMG_2008_8_2_a5/

[1] D. Kolton, R. Kress, Metody integralnykh uravnenii v teorii rasseyaniya, Mir, M., 1987, 311 pp. | MR

[2] Liu Changmei, The Helmholtz equation on Lipschitz domains, PhD Thesis Department of Mathematics, University of North Carolina, 1995

[3] T. S. Angell, A. Kirsch, Optimization methods in electromagnetic radiation, Springer, 2003 | MR

[4] A. Habbal, “Nonsmooth Shape Optimization Applied to Linear Acoustics”, SIAM Journal on Optimization, 8:4 (1998), 989–1006 | DOI | MR | Zbl

[5] Cao Yanzhao, D. Stanescu, “Shape optimization for noise radiation problems”, Computers and Mathematics with Applications, 44 (2002), 1527–1537 | DOI | MR | Zbl

[6] 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 | MR | Zbl

[7] J. Jahn, A. Kirsch, C. Wagner, “Optimization of rod antennas of mobile phones”, Math. Meth. Oper. Res., 59 (2004), 37–51 | DOI | MR | Zbl

[8] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980, 496 pp. | MR | Zbl

[9] A. D. Ioffe, V. M. Tikhomirov, Teoriya ekstremalnykh zadach, Nauka, M., 1974, 240 pp. | MR | Zbl

[10] A. V. Fursikov, Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999, 352 pp.