메뉴 건너뛰기




Volumn 203, Issue 2, 2012, Pages 153-182

Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide

Author keywords

Acoustic waveguide; Asymptotic behaviour; Augmented scattering matrix.; Eigenvalues in the continuous spectrum; Water waves in a channel

Indexed keywords


EID: 84859575907     PISSN: 10645616     EISSN: None     Source Type: Journal    
DOI: 10.1070/SM2012v203n02ABEH004217     Document Type: Article
Times cited : (26)

References (39)
  • 3
    • 0003218752 scopus 로고
    • The boundary value problems of mathematical physics, Nauka, Moscow 1973 English transl
    • Springer-Verlag, New York
    • O. A. Ladyzhenskaya, The boundary value problems of mathematical physics, Nauka, Moscow 1973; English transl., Appl. Math. Sci., vol. 49, Springer-Verlag, New York 1985.
    • (1985) Appl. Math. Sci. , vol.49
    • Ladyzhenskaya, O.A.1
  • 4
    • 0003647398 scopus 로고
    • Spectral-theory of self-adjoint operators in Hilbert space, Leningrad State University Publishing House, Leningrad 1980; English transl
    • Kluwer Acad. Publ., Dordrecht
    • M. S. Birman and M. Z. Solomyak, Spectral-theory of self-adjoint operators in Hilbert space, Leningrad State University Publishing House, Leningrad 1980; English transl., Math. Appl. (Soviet Ser.), Kluwer Acad. Publ., Dordrecht 1987.
    • (1987) Math. Appl. (Soviet Ser.)
    • Birman, M.S.1    Solomyak, M.Z.2
  • 5
    • 0345853685 scopus 로고
    • 2u = 0 with boundary conditions on equidistant curves and the propagation of electromagnetic waves in a waveguide
    • 2u = 0 with boundary conditions on equidistant curves and the propagation of electromagnetic waves in a waveguide", Dokl. Akad. Nauk SSSR 123:4 (1958), 631-633;
    • (1958) Dokl. Akad. Nauk SSSR , vol.123 , Issue.4 , pp. 631-633
    • Maslov, V.P.1
  • 6
    • 8144223674 scopus 로고
    • English transl.
    • English transl. in Soviet Physics. Dokl. 3 (1959), 1132-1135.
    • (1959) Soviet Physics. Dokl. , vol.3 , pp. 1132-1135
  • 7
    • 0002570054 scopus 로고
    • Curvature-induced bound states in quantum waveguides in two and three dimensions
    • P. Duclos and P. Exner, "Curvature-induced bound states in quantum waveguides in two and three dimensions", Rev. Math. Phys. 7:1 (1995), 73-102.
    • (1995) Rev. Math. Phys. , vol.7 , Issue.1 , pp. 73-102
    • Duclos, P.1    Exner, P.2
  • 9
    • 29144529116 scopus 로고    scopus 로고
    • Local perturbations of quantum waveguides
    • R. R. Gadyl'shin, "Local perturbations of quantum waveguides", Teor. Mat. Fiz. 145:3 (2005), 358-371;
    • (2005) Teor. Mat. Fiz. , vol.145 , Issue.3 , pp. 358-371
    • Gadyl'shin, R.R.1
  • 10
    • 29144529116 scopus 로고    scopus 로고
    • English transl
    • English transl. in Theoret. and Math. Phys. 145:3 (2005), 1678-1690.
    • (2005) Theoret. and Math. Phys. , vol.145 , Issue.3 , pp. 1678-1690
  • 11
    • 77958530305 scopus 로고    scopus 로고
    • Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold
    • S. A. Nazarov, "Variational and asymptotic methods for finding eigenvalues below the continuous spectrum threshold", Sibirsk. Mat. Zh. 51:5 (2010), 1086-1101;
    • (2010) Sibirsk. Mat. Zh. , vol.51 , Issue.5 , pp. 1086-1101
    • Nazarov, S.A.1
  • 12
    • 77958530305 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Sib. Math. J. 51:5 (2010), 866-878.
    • (2010) Sib. Math. J. , vol.51 , Issue.5 , pp. 866-878
  • 14
    • 0008994366 scopus 로고    scopus 로고
    • Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. I
    • I. V. Kamotskií and S.A. Nazarov, "Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. I", Mat. Sb. 190:1 (1999), 109-138;
    • (1999) Mat. Sb. , vol.190 , Issue.1 , pp. 109-138
    • Kamotskií, I.V.1    Nazarov, S.A.2
  • 15
    • 0033246621 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Sb. Math. 190:1 (1999), 111-141.
    • (1999) Sb. Math. , vol.190 , Issue.1 , pp. 111-141
  • 16
    • 0010969767 scopus 로고    scopus 로고
    • Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. II
    • I. V. Kamotskií and S.A. Nazarov, "Wood's anomalies and surface waves in the problem of scattering by a periodic boundary. II", Mat. Sb. 190:2 (1999), 43-70;
    • (1999) Mat. Sb. , vol.190 , Issue.2 , pp. 43-70
    • Kamotskií, I.V.1    Nazarov, S.A.2
  • 17
    • 0033246627 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Sb. Math. 190:2 (1999), 205-231.
    • (1999) Sb. Math. , vol.190 , Issue.2 , pp. 205-231
  • 18
    • 0009079814 scopus 로고
    • Selfadjoint elliptic problems: The scattering operator and the polarization operator on edges of the boundary
    • Plamenevsky)
    • S. A. Nazarov and B.A. Plamenevskij (Plamenevsky), "Selfadjoint elliptic problems: The scattering operator and the polarization operator on edges of the boundary", Algebra i Analiz 6:4 (1994), 157-186;
    • (1994) Algebra i Analiz , vol.6 , Issue.4 , pp. 157-186
    • Nazarov, S.A.1    Plamenevskij, B.A.2
  • 19
    • 0037906007 scopus 로고
    • English transl.
    • English transl. in St. Petersburg Math. J. 6:4 (1995), 839-863.
    • (1995) St. Petersburg Math. J. , vol.6 , Issue.4 , pp. 839-863
  • 20
    • 33744788213 scopus 로고    scopus 로고
    • English transl.
    • English transl. in J. Math. Sci. (New York) 111:4 (2002), 3657-3666.
    • (2002) J. Math. Sci. (New York) , vol.111 , Issue.4 , pp. 3657-3666
  • 22
    • 35648955038 scopus 로고    scopus 로고
    • Embedded trapped modes in water waves and acoustics
    • DOI 10.1016/j.wavemoti.2007.04.009, PII S0165212507000376, Localization of Wave Motion
    • C. M. Linton and P. McIver, "Embedded trapped modes in water waves and acoustics", Wave motion 45:1-2 (2007), 16-29. (Pubitemid 350028631)
    • (2007) Wave Motion , vol.45 , Issue.1-2 , pp. 16-29
    • Linton, C.M.1    McIver, P.2
  • 23
    • 84979114206 scopus 로고
    • Scattering theory for diffraction gratings
    • Springer-Verlag, New York
    • C. H. Wilcox, Scattering theory for diffraction gratings, Appl. Math. Sci., vol. 46, Springer-Verlag, New York 1984.
    • (1984) Appl. Math. Sci. , vol.46
    • Wilcox, C.H.1
  • 24
    • 0003331317 scopus 로고
    • Elliptic problems in domains with piecewise smooth boundaries
    • de Gruyter, Berlin
    • S. A. Nazarov and B.A. Plamenevsky, Elliptic problems in domains with piecewise smooth boundaries, de Gruyter Exp. Math., vol. 13, de Gruyter, Berlin 1994.
    • (1994) De Gruyter Exp. Math. , vol.13
    • Nazarov, S.A.1    Plamenevsky, B.A.2
  • 25
    • 0000309125 scopus 로고
    • Boundary value problems for elliptic equations in domains with conical or corner points
    • Moscow University Publishing House, Moscow (Russian
    • V.A. Kondrat'ev, "Boundary value problems for elliptic equations in domains with conical or corner points", Tr. Mosk. Mat. Obshch., vol. 16, Moscow University Publishing House, Moscow 1963, pp. 219-292. (Russian
    • (1963) Tr. Mosk. Mat. Obshch. , vol.16 , pp. 219-292
    • Kondrat'ev, V.A.1
  • 27
    • 0002787469 scopus 로고
    • Coefficients of asymptotic expressions for solutions of elliptic boundary value problems in domains with conical points
    • Russian
    • V.G. Maz'ya and B. A. Plamenevsky, "Coefficients of asymptotic expressions for solutions of elliptic boundary value problems in domains with conical points", Math. Nachr. 76:1 (1977), 29-60. (Russian
    • (1977) Math. Nachr. , vol.76 , Issue.1 , pp. 29-60
    • Maz'ya, V.G.1    Plamenevsky, B.A.2
  • 28
    • 0002688101 scopus 로고
    • Estimates in Lp and Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary
    • Russian
    • V.G. Maz'ya and B. A. Plamenevsky, "Estimates in Lp and Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary", Math. Nachr. 77:1 (1978), 25-82. (Russian
    • (1978) Math. Nachr. , vol.77 , Issue.1 , pp. 25-82
    • Maz'ya, V.G.1    Plamenevsky, B.A.2
  • 29
    • 0013143625 scopus 로고    scopus 로고
    • The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes
    • S. A. Nazarov, "The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes", Uspekhi Mat. Nauk 54:5 (1999), 77-142;
    • (1999) Uspekhi Mat. Nauk , vol.54 , Issue.5 , pp. 77-142
    • Nazarov, S.A.1
  • 30
    • 0033262908 scopus 로고    scopus 로고
    • Russian Math. Surveys 54:5 (1999), 947-1014.
    • (1999) Russian Math. Surveys , vol.54 , Issue.5 , pp. 947-1014
  • 31
    • 84859567753 scopus 로고    scopus 로고
    • Calculation of characteristics of trapped modes in T-shaped waveguides
    • S. A. Nazarov and A. V. Shanin, "Calculation of characteristics of trapped modes in T-shaped waveguides", Zh. Vychisl. Mat. Mat. Fiz. 51:1 (2011), 104-119;
    • (2011) Zh. Vychisl. Mat. Mat. Fiz. , vol.51 , Issue.1 , pp. 104-119
    • Nazarov, S.A.1    Shanin, A.V.2
  • 33
    • 84980075953 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
    • S. Agmon, A. Douglis and L. Nirenberg, "Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I", Comm. Pure Appl. Math. 12:4 (1959), 623-727.
    • (1959) Comm. Pure Appl. Math. , vol.12 , Issue.4 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 34
    • 44149097519 scopus 로고    scopus 로고
    • Artificial boundary conditions for finding surface waves in the problem of diffraction by a periodic boundary
    • S. A. Nazarov, "Artificial boundary conditions for finding surface waves in the problem of diffraction by a periodic boundary", Zh. Vychisl. Mat. Mat. Fiz. 46:12 (2006), 2265-2276;
    • (2006) Zh. Vychisl. Mat. Mat. Fiz. , vol.46 , Issue.12 , pp. 2265-2276
    • Nazarov, S.A.1
  • 35
    • 33846136735 scopus 로고    scopus 로고
    • Comput. Math. Math. Phys. 46:12 (2006), 2164-2175.
    • (2006) Comput. Math. Math. Phys. , vol.46 , Issue.12 , pp. 2164-2175
  • 37
    • 84859590803 scopus 로고
    • English transl. Amer. Math. Soc., Providence, RI
    • English transl., Transl. Math. Monogr., vol. 102, Amer. Math. Soc., Providence, RI 1992.
    • (1992) Transl. Math. Monogr. , vol.102
  • 38
    • 0004132033 scopus 로고
    • Nauka, Moscow English Transl Pergamon Press, Oxford 1982
    • L. V. Kantorovich and G.P. Akilov, Functional analysis, Nauka, Moscow 1977; English transl., Pergamon Press, Oxford 1982.
    • (1977) Functional Analysis
    • Kantorovich, L.V.1    Akilov, G.P.2
  • 39
    • 0010969483 scopus 로고
    • Radiation principles for selfadjoint elliptic problems
    • Leningrad State University Puiblishing House, Leningrad (Russian
    • S. A. Nazarov and B.A. Plamenevsky, "Radiation principles for selfadjoint elliptic problems", Differential equations. Spectral theory, Probl. Mat. Fiz., vol. 13, Leningrad State University Puiblishing House, Leningrad 1991, pp. 192-244. (Russian)
    • (1991) Differential Equations. Spectral Theory, Probl. Mat. Fiz. , vol.13 , pp. 192-244
    • Nazarov, S.A.1    Plamenevsky, B.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.