Geodesic
On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 9, pp. 1587-1597 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of determining the permittivity of material samples of arbitrary shape placed in a rectangular waveguide with perfectly conducting walls is investigated. The problem is reduced to solving a nonlinear volume singular integral equation. A theorem on the existence and uniqueness of solutions to the nonlinear volume singular integral equation and of the inverse boundary value problem for determining the permittivity of the material is proved. 
@article{ZVMMF_2010_50_9_a3,
     author = {D. A. Mironov and Yu. G. Smirnov},
     title = {On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1587--1597},
     year = {2010},
     volume = {50},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_9_a3/}
}
TY  - JOUR
AU  - D. A. Mironov
AU  - Yu. G. Smirnov
TI  - On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1587
EP  - 1597
VL  - 50
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_9_a3/
LA  - ru
ID  - ZVMMF_2010_50_9_a3
ER  - 
%0 Journal Article
%A D. A. Mironov
%A Yu. G. Smirnov
%T On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1587-1597
%V 50
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_9_a3/
%G ru
%F ZVMMF_2010_50_9_a3
D. A. Mironov; Yu. G. Smirnov. On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 9, pp. 1587-1597. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_9_a3/

[1] Shestopalov Yu. V., Smirnov Yu. G., Yakovlev V. V., “Volume singular integral equation method for determination of effective permittivity of meta- and nanomaterials”, PIERS'2008, Proc. Progress in Electromagnetics Res. Symp. (Cambridge, MA, Jule 2–6, 2008), 291–292

[2] Samokhin A. B., Integralnye uravneniya i iteratsionnye metody v elektromagnitnom rasseyanii, Radio i svyaz, M., 1998

[3] Smirnov Yu. G., Tsupak A. A., “Issledovanie elektromagnitnoi zadachi difraktsii na dielektricheskom tele metodom ob'emnogo singulyarnogo integralnogo uravneniya”, Zh. vychisl. matem. i matem. fiz., 44:12 (2004), 2252–2267 | MR | Zbl

[4] Smirnov Yu. G., “Primenenie GRID tekhnologii dlya resheniya nelineinogo ob'emnogo singulyarnogo integralnogo uravneniya dlya opredeleniya effektivnoi dielektricheskoi pronitsaemosti nanomaterialov”, Izv. vuzov. Povolzhskii region. Fiz.-matem. nauki, 2008, no. 3, 39–55

[5] Smirnov Yu. G., Matematicheskie metody issledovaniya zadach elektrodinamiki, Informatsionno-izdat. tsentr PGU, Penza, 2009

[6] Kobayashi K., Shestopalov Yu. V., Smirnov Yu. G., “Investigation of electromagnetic diffraction by a dielectric body in a waveguide using the method of volume singular integral equation”, SIAM J. Appl. Math., 70:3 (2009), 969–983 | DOI | MR | Zbl

[7] Smirnov Yu. G., “Inverse boundary value problem for determination of permittivity of dielectric body in a waveguide using the method of volume singular integral equation”, IEEJ Trans. Fundamentals and Materials, 129:10 (2009), 675–680 | DOI

[8] Smirnov Yu. G., “O suschestvovanii i edinstvennosti reshenii obratnoi kraevoi zadachi dlya opredeleniya effektivnoi dielektricheskoi pronitsaemosti nanomaterialov”, Izv. vuzov. Povolzhskii region. Fiz.-matem. nauki, 2009, no. 1, 11–24

[9] Vasyunin D. I., Medvedik M. Yu., Smirnov Yu. G., “Metod kollokatsii resheniya ob'emnogo singulyarnogo integralnogo uravneniya v zadache opredeleniya dielektricheskoi pronitsaemosti materiala”, Izv. vuzov. Povolzhskii region. Fiz.-matem. nauki, 2009, no. 3, 68–78

[10] Valovik D. V., Smirnov Yu. G., “Metod psevdodifferentsialnykh operatorov dlya issledovaniya ob'emnogo singulyarnogo integralnogo uravneniya”, Izv. vuzov. Povolzhskii region. Fiz.-matem. nauki, 2009, no. 4, 102–114

[11] Ilinskii A. S., Smirnov Yu. G., Difraktsiya elektromagnitnykh voln na provodyaschikh ekranakh, IPRZhR, M., 1996

[12] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1993 | MR | Zbl