Geodesic
Nonreflecting distortions of an isotropic strip clamped between rigid punches
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1698-1708 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The sides of a homogeneous and isotropic strip are considered that are in ideal contact with infinite rigid punches. Smooth distortions of the sides are constructed so that, at one or several given frequencies, an elastic wave propagating through waveguide gives rise to only exponentially decaying perturbations and, possibly, to a small phase shift. 
@article{ZVMMF_2013_53_10_a9,
     author = {S. A. Nazarov},
     title = {Nonreflecting distortions of an isotropic strip clamped between rigid punches},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1698--1708},
     year = {2013},
     volume = {53},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_10_a9/}
}
TY  - JOUR
AU  - S. A. Nazarov
TI  - Nonreflecting distortions of an isotropic strip clamped between rigid punches
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 1698
EP  - 1708
VL  - 53
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_10_a9/
LA  - ru
ID  - ZVMMF_2013_53_10_a9
ER  - 
%0 Journal Article
%A S. A. Nazarov
%T Nonreflecting distortions of an isotropic strip clamped between rigid punches
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 1698-1708
%V 53
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_10_a9/
%G ru
%F ZVMMF_2013_53_10_a9
S. A. Nazarov. Nonreflecting distortions of an isotropic strip clamped between rigid punches. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1698-1708. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_10_a9/

[1] Fikera G., Teoremy suschestvovaniya v teorii uprugosti, Mir, M., 1974

[2] Kostrov B. V., “Difraktsiya ploskoi volny na zhestkom kline, vstavlennom bez treniya v bezgranichnuyu upruguyu sredu”, Prikl. matem. i mekhan., 30:1 (1966), 198–203 | Zbl

[3] Nazarov S. A., “Asimptotika sobstvennykh chisel na nepreryvnom spektre regulyarno vozmuschennogo kvantovogo volnovoda”, Teor. i matem. fiz., 167:2 (2011), 239–262 | DOI

[4] Nazarov S. A., “Prinuditelnaya ustoichivost sobstvennogo znacheniya na nepreryvnom spektre volnovoda s prepyatstviem”, Zh. vychisl. matem. i matem. fiz., 52:3 (2012), 521–538 | Zbl

[5] Bonne-Ben Dia A.-S., Nazarov S. A., “Prepyatstviya v akusticheskom volnovode, stanovyaschiesya “nevidimymi” na zadannykh chastotakh”, Akusticheskii zhurnal, 59:6 (2013)

[6] Nazarov S. A., Plamenevsky B. A., Elliptic problems in domains with piecewise smooth boundaries, Walter de Gruyter, Berlin–New York, 1994 | MR

[7] Umov N. A., Uravneniya dvizheniya energii v telakh, Tipogr. Ulrikha i Shultse, Odessa, 1874

[8] Vorovich I. I., Babeshko V. A., Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastei, Nauka, M., 1979 | MR

[9] Greenleaf A., Kurylev Ya., Lassas M., Uhlmann G., “Invisibility and inverse problems”, Bull. Amer. Math. Soc., 46:1 (2009), 55–97 | DOI | MR | Zbl

[10] Maz'ya V., Nazarov S., Plamenevskij B., Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, v. 1, Birkhäuser Verlag, Basel, 2000

[11] Nazarov S. A., “Sobstvennye chisla operatora Laplasa s usloviyami Neimana na regulyarno vozmuschennykh stenkakh volnovoda”, Probl. matem. analiza, 53, Novosibirsk, 2011, 104–119

[12] Nazarov S. A., “Asimptotika reshenii i modelirovanie zadach teorii uprugosti v oblasti s bystroostsilliruyuschei granitsei”, Izv. RAN. Seriya matem., 72:3 (2008), 103–158 | DOI | MR | Zbl

[13] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, IL, M., 1962

[14] Wood R. W., “On a remarkable case of uneven distribution of light in a diffraction grating spectrum”, Philosophical Magazine. Series 6, 4:21 (1902), 396–402 | DOI

[15] Hessel A., Oliner A. A., “A new theory of Wood's anomalies on optical gratings”, Applied Optics, 4:10 (1965), 1275–1297 | DOI

[16] Nazarov S. A., “Asimptotika sobstvennogo chisla volnovoda s tonkim ekraniruyuschim prepyatstviem i anomalii Vuda”, Zapiski nauchn. seminarov POMI RAN, 385, 2010, 98–134 | MR