Geodesic
Calculation of characteristics of trapped modes in T-shaped waveguides
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 1, pp. 104-119 Cet article a éte moissonné depuis la source Math-Net.Ru

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The spectrum of the Dirichlet problem for the Laplace operator in a plane T-shaped waveguide is investigated. The critical width of the half-strip branch is determined such that, if the width is greater, the waveguide has no discrete spectrum. The existence of a critical width is proved the oretically. 
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S. A. Nazarov; A. V. Shanin. Calculation of characteristics of trapped modes in T-shaped waveguides. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 1, pp. 104-119. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a7/

[1] Wilcox C., Scattering theory for diffraction gratings, Springer, Berlin, 1980 | MR

[2] Nazarov S. A., Plamenevskii B. A., Ellipticheskie zadachi v oblastyakh s kusochno gladkoi granitsei, Nauka, M., 1991; Nazarov S. A., Plamenevsky B. A., Elliptic problems in domains with piecewise smooth boundaries, Walter de Gruyter, Berlin, New York, 1994 | MR

[3] Nazarov S. A., “Lokalizovannye volny v T-obraznom volnovode”, Akustich. zhurnal, 56:6 (2010), 747–758

[4] Tsynkov S. V., “Numerical solution of problems on unbounded domains”, Appl. Numer. Math., 27 (1998), 465–532 | DOI | MR | Zbl

[5] Birman M. Sh., Solomyak M. Z., Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Izd-vo LGU, L., 1980 | MR

[6] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[7] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. Mosk. matem. ob-va, 16, 1963, 219–292

[8] Mazya V. G., Plamenevskii B. A., “O koeffitsientakh v asimptotike reshenii ellipticheskikh kraevykh zadach v oblasti s konicheskimi tochkami”, Math. Nachricht., 76 (1977), 29–60 | DOI

[9] Mazya V. G., Plamenevskii B. A., “Otsenki v $L_p$ i v klassakh Geldera i printsip maksimuma Miranda–Agmona dlya reshenii ellipticheskikh kraevykh zadach v oblastyakh s osobymi tochkami na granitse”, Math. Nachricht., 77 (1977), 25–82 | MR

[10] Nazarov S. A., “Polinomialnoe svoistvo samosopryazhennykh ellipticheskikh kraevykh zadach i algebraicheskoe opisanie ikh atributov”, Uspekhi matem. nauk, 54:5 (1999), 77–142 | MR | Zbl

[11] Mikhlin S. G., Lineinye uravneniya v chastnykh proizvodnykh, Vyssh. shkola, M., 1977 | MR

[12] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[13] Mazja W. G., Nasarow S. A., Plamenewski B. A., Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten, v. 1, Akad. Verlag, Berlin, 1991; Maz'ya V., Nazarov S., Plamenevskij B., Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, v. 1, Birkhäuser, Basel, 2000

[14] Nazarov S. A., “Ob asimptotike po parametru resheniya ellipticheskoi kraevoi zadachi s periodicheskimi koeffitsientami v tsilindre”, Differents. ur-niya i ikh primeneniya, 30, Izd-vo AN LitSSR, Vilnyus, 1981, 27–46

[15] Nazarov S. A., “The Navier–Stokes problem in thin or long tubes with periodically varying cross-section”, ZAMM, 80:9 (2000), 591–612 | 3.0.CO;2-Q class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[16] Lebedev V. I., Agoshkov V. I., Operatory Puankare–Steklova i ikh prilozheniya v analize, Izdanie Otd. vychisl. matem. AN SSSR, M., 1983 | MR | Zbl