Geodesic
Inverse extremal problems for the Maxwell equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1038-1046 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem is studied of recovering the impedance function involved multiplicatively in boundary conditions for Maxwell’s equations. The inverse problem is reduced to an extremum one. The solvability of the extremum problem is proved, an optimality system is derived, and sufficient conditions for the local uniqueness and stability of its solution are established. 
@article{ZVMMF_2010_50_6_a5,
     author = {R. V. Brizitskiǐ and A. S. Savenkova},
     title = {Inverse extremal problems for the {Maxwell} equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1038--1046},
     year = {2010},
     volume = {50},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a5/}
}
TY  - JOUR
AU  - R. V. Brizitskiǐ
AU  - A. S. Savenkova
TI  - Inverse extremal problems for the Maxwell equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1038
EP  - 1046
VL  - 50
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a5/
LA  - ru
ID  - ZVMMF_2010_50_6_a5
ER  - 
%0 Journal Article
%A R. V. Brizitskiǐ
%A A. S. Savenkova
%T Inverse extremal problems for the Maxwell equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1038-1046
%V 50
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a5/
%G ru
%F ZVMMF_2010_50_6_a5
R. V. Brizitskiǐ; A. S. Savenkova. Inverse extremal problems for the Maxwell equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1038-1046. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a5/

[1] Caconi F., Colton D., Haddar H., “The linear sampling method for anisotropic media”, J. Comput. Appl. Math., 146 (2003), 285–299 | DOI | MR

[2] Caconi F., Colton D., “A uniqueness theorem for an inverse electromagnetic scattering problem in inhomogeneous anisotropic media”, Proc. Edinburg Math. Soc., 46 (2003), 293–314 | DOI | MR

[3] Cakoni F., Colton D., Monk P., “The electromagnetic inverse scattering problem for partially coated Lipschitz domains”, Proc. Edinburg Math. Soc., 134 (2004), 661–682 | DOI | MR | Zbl

[4] Cakoni F., Haddar H., “Identification of partially coated anisotropic buried objects using electromagnetic Cauchy data”, J. Integral Equations Appl., 134:3 (2007), 359–389 | DOI | MR

[5] Costabel M., “A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains”, Math. Meth. Appl. Sci., 12 (1990), 365–368 | DOI | MR | Zbl

[6] Costable M., Dauge M., “On resultat de densite pour les equations de Maxwell regularisees dans undomain lipschitzien”, C. R. acad. Sci. Paris, 327 (1998), 849–854 | MR

[7] Colton D., Kress R., Inverse acoustic and electromagnetic scattering theory, 2nd ed., Springer, Berlin, 1998 | MR | Zbl

[8] Leis R., Initial boundary value problems in mathematical physics, John Wiley Sons, New York, 1996 | MR

[9] Alekseev G. V., Chebotarev A. Yu., “Obratnye zadachi akusticheskogo potentsiala”, Zh. vychisl. matem. i matem. fiz., 25:8 (1985), 1189–1199 | MR

[10] Alekseev G. V., “Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teplovoi konvektsii”, Vestn. NGU. Matem., mekhan. i informatika, 6:2 (2006), 6–32

[11] Alekseev G. V., “Koeffitsientnye obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teplomassoperenosa”, Zh. vychisl. matem. i matem. fiz., 47:6 (2007), 1055–1076 | MR

[12] Savenkova S. A., “Asimptotika optimalnogo upravleniya v zadache rasseyaniya garmonicheskikh voln na prepyatstvii”, Zh. vychisl. matem. i matem. fiz., 47:9 (2007), 1635–1641 | MR

[13] Savenkova A. S., “Multiplikativnoe upravlenie v zadache rasseyaniya dlya uravneniya Gelmgoltsa”, Sibirskii zhurnal industr. matem., 10:1 (2007), 128–139 | MR

[14] Alekseev G. V., Soboleva O. V., Tereshko D. A., “Zadachi identifikatsii dlya statsionarnoi modeli massoperenosa”, Prikl. mekhan. i tekhn. fiz., 49:4 (2008), 24–35 | MR

[15] Brizitskii R. V., Savenkova S. A., “Asimptotika reshenii zadach multiplikativnogo upravleniya dlya ellipticheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 48:9 (2008), 1607–1618 | MR

[16] Brizitskii R. V., Kozhushnaya E. R., “Edinstvennost resheniya koeffitsientnoi obratnoi ekstremalnoi zadachi dlya uravneniya konvektsii-diffuzii-reaktsii”, Dalnevost. matem. zhurnal, 8:2 (2008), 3–11 | MR

[17] Valli A., Orthogonal decompositions of $\mathbf{L}^2(\Omega)^3$, Preprint UTM 493, Dept. Math. Univ. Toronto, Galamen, 1995

[18] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl

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

[20] Sea Zh., Optimizatsiya.Teoriya i algoritmy, Mir, M., 1973