메뉴 건너뛰기




Volumn 45, Issue 5, 2011, Pages 947-979

Radiation conditions at the top of a rotational cusp in the theory of water-waves

Author keywords

Cuspidal domain; Linear water wave problem; Radiation condition; Scattering matrix

Indexed keywords

MATHEMATICAL OPERATORS; MATRIX ALGEBRA; SURFACE WATERS;

EID: 80052017313     PISSN: 28227840     EISSN: 28047214     Source Type: Journal    
DOI: 10.1051/m2an/2011004     Document Type: Article
Times cited : (26)

References (56)
  • 1
    • 70349975614 scopus 로고    scopus 로고
    • On the structure of the spectrum of the elasticity problem for a body with a super-sharp spike
    • F.L. Bakharev and S.A. Nazarov, On the structure of the spectrum of the elasticity problem for a body with a super-sharp spike. Sibirsk. Mat. Zh. 50 (2009) 746-756.
    • (2009) Siberian Math. J. , vol.50 , pp. 746-756
    • Bakharev, F.L.1    Nazarov, S.A.2
  • 4
    • 68149175195 scopus 로고    scopus 로고
    • Asymptotics of solutions of the Neumann problem in a domain with closely posed components of the boundary
    • G. Cardone, S.A. Nazarov and J. Sokolowski, Asymptotics of solutions of the Neumann problem in a domain with closely posed components of the boundary. Asymptotic Analysis 62 (2009) 41-88.
    • (2009) Asymptotic Analysis , vol.62 , pp. 41-88
    • Cardone, G.1    Nazarov, S.A.2    Sokolowski, J.3
  • 5
    • 63449109236 scopus 로고    scopus 로고
    • The "absorption" effect caused by beak-shaped boundary irregularity for elastic waves
    • G. Cardone, S.A. Nazarov and J. Taskinen, The "absorption" effect caused by beak-shaped boundary irregularity for elastic waves. Dokl. Ross. Akad. Nauk. 425 (2009) 182-186.
    • (2009) Dokl. Ross. Akad. Nauk. , vol.425 , pp. 182-186
    • Cardone, G.1    Nazarov, S.A.2    Taskinen, J.3
  • 6
    • 63449109236 scopus 로고    scopus 로고
    • (English transl. Doklady Physics 54 (2009) 146-150.)
    • (2009) Doklady Physics , vol.54 , pp. 146-150
  • 7
    • 72149108716 scopus 로고    scopus 로고
    • Criteria for the existence of the essential spectrum for beak-shaped elastic bodies
    • to appear
    • G. Cardone, S.A. Nazarov and J. Taskinen, Criteria for the existence of the essential spectrum for beak-shaped elastic bodies. J. Math. Pures Appl. (to appear)
    • J. Math. Pures Appl.
    • Cardone, G.1    Nazarov, S.A.2    Taskinen, J.3
  • 8
    • 23044518707 scopus 로고    scopus 로고
    • Robin boundary value problems on arbitrary domains
    • D. Daners, Robin boundary value problems on arbitrary domains. Trans. Amer. Math. Soc. 352 (2000) 4207-4236.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 4207-4236
    • Daners, D.1
  • 9
    • 33745598153 scopus 로고    scopus 로고
    • A Faber-Krahn inequality for Robin problems in any space dimension
    • DOI 10.1007/s00208-006-0753-8
    • D. Daners, A Faber-Krahn inequality for Robin problems in any space dimension. Math. Annal. 335 (2006) 767-785. (Pubitemid 43992023)
    • (2006) Mathematische Annalen , vol.335 , Issue.4 , pp. 767-785
    • Daners, D.1
  • 11
    • 84959654606 scopus 로고
    • The eigenvalues of ∇2u+λ u=0 when the boundary conditions are given on semi-infinite domains
    • D.S. Jones, The eigenvalues of ∇ 2u+λ u=0 when the boundary conditions are given on semi-infinite domains. Proc. Camb. Phil. Soc. 49 (1953) 668-684.
    • (1953) Proc. Camb. Phil. Soc. , vol.49 , pp. 668-684
    • Jones, D.S.1
  • 12
    • 0000309125 scopus 로고
    • Boundary value problems for elliptic problems in domains with conical or corner points
    • V.A. Kondratiev, Boundary value problems for elliptic problems in domains with conical or corner points. Trudy Moskov. Mat. Obshch. 16 (1967) 209-292. )
    • (1967) Trudy Moskov. Mat. Obshch. , vol.16 , pp. 209-292
    • Kondratiev, V.A.1
  • 13
    • 0000309125 scopus 로고
    • English transl. Trans. Moscow Mat. Soc. 16 (1967) 227-313
    • (1967) Trans. Moscow Mat. Soc. , vol.16 , pp. 227-313
  • 14
    • 0003366106 scopus 로고    scopus 로고
    • Elliptic boundary value problems in domains with point singularities
    • American Mathematical Society, Providence, RI
    • V.A. Kozlov, V.G. Maz'ya and J. Rossmann, Elliptic boundary value problems in domains with point singularities. Mathematical Surveys and Monographs 52. American Mathematical Society, Providence, RI (1997).
    • (1997) Mathematical Surveys and Monographs , vol.52
    • Kozlov, V.A.1    Maz'Ya, V.G.2    Rossmann, J.3
  • 15
    • 0003325353 scopus 로고    scopus 로고
    • Spectral problems associated with corner singularities of solutions to elliptic equations
    • American Mathematical Society, Providence, RI
    • V.A. Kozlov, V.G. Maz'ya and J. Rossmann, Spectral problems associated with corner singularities of solutions to elliptic equations. Mathematical Surveys and Monographs 85. American Mathematical Society, Providence, RI (2001).
    • (2001) Mathematical Surveys and Monographs , vol.85
    • Kozlov, V.A.1    Maz'Ya, V.G.2    Rossmann, J.3
  • 16
    • 6344237145 scopus 로고    scopus 로고
    • New type of vibration dampers utilising the effect of acoustic "black holes
    • V.V. Krylov, New type of vibration dampers utilising the effect of acoustic "black holes". Acta Acustica united with Acustica 90 (2004) 830-837.
    • (2004) Acta Acustica United with Acustica , vol.90 , pp. 830-837
    • Krylov, V.V.1
  • 20
    • 0003796632 scopus 로고
    • translated from the Russian by T.O. Shaposhnikova. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin
    • V. Mazya, Sobolev spaces, translated from the Russian by T.O. Shaposhnikova. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin (1985).
    • (1985) Sobolev Spaces
    • Mazya, V.1
  • 21
    • 0009222632 scopus 로고
    • The asymptotic behavior of solutions of differential equations in Hilbert space
    • erratum, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 709-710.
    • V.G. Maz'ya and B.A. Plamenevskii, The asymptotic behavior of solutions of differential equations in Hilbert space. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972) 1080-1133; erratum, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 709-710.
    • (1972) (Russian) Izv. Akad. Nauk SSSR Ser. Mat. , vol.36 , pp. 1080-1133
    • Maz'Ya, V.G.1    Plamenevskii, B.A.2
  • 22
    • 0002787469 scopus 로고
    • On coefficients in asymptotics of solutions of elliptic boundary value problems in a domain with conical points
    • V.G, Mazja and B.A. Plamenevskii, On coefficients in asymptotics of solutions of elliptic boundary value problems in a domain with conical points. Math. Nachr. 76 (1977) 29-60.
    • (1977) Math. Nachr. , vol.76 , pp. 29-60
    • Mazja, V.G.1    Plamenevskii, B.A.2
  • 24
    • 0002688101 scopus 로고
    • p and Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary
    • p 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. 81 (1978) 25-82.
    • (1978) Math. Nachr. , vol.81 , pp. 25-82
    • Mazja, V.G.1    Plamenevskii, B.A.2
  • 27
    • 3042686028 scopus 로고
    • Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval
    • M.A. Mironov, Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval. Soviet Physics-Acoustics 34 (1988) 318-319.
    • (1988) Soviet Physics-Acoustics , vol.34 , pp. 318-319
    • Mironov, M.A.1
  • 28
    • 0009224091 scopus 로고
    • Asymptotics of the solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain
    • S.A. Nazarov Asymptotics of the solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain. Izv. Ross. Akad. Nauk. Ser. Mat. 58 (1994) 92-120.
    • (1994) Izv. Ross. Akad. Nauk. Ser. Mat. , vol.58 , pp. 92-120
    • Nazarov, S.A.1
  • 29
    • 80051987642 scopus 로고
    • (English transl. Math. Izvestiya 44 (1995) 91-118.)
    • (1995) Math. Izvestiya , vol.44 , pp. 91-118
  • 30
    • 33645031622 scopus 로고
    • On the flow of water under a still stone
    • S.A. Nazarov, On the flow of water under a still stone. Mat. Sbornik 186 (1995) 75-110.
    • (1995) Mat. Sbornik , vol.186 , pp. 75-110
    • Nazarov, S.A.1
  • 31
    • 80051969151 scopus 로고
    • English transl. Math. Sbornik 186 (1995) 1621-1658.)
    • (1995) Math. Sbornik , vol.186 , pp. 1621-1658
  • 32
    • 0002364556 scopus 로고
    • A general scheme for averaging self-adjoint elliptic systems in multidimensional domains, including thin domains
    • S.A. Nazarov, A general scheme for averaging self-adjoint elliptic systems in multidimensional domains, including thin domains. Algebra Analiz. 7 (1995) 1-92.
    • (1995) Algebra Analiz. , vol.7 , pp. 1-92
    • Nazarov, S.A.1
  • 33
    • 0040335157 scopus 로고    scopus 로고
    • (English transl.St. Petersburg Math. J. 7. (1996) 681-748)
    • (1996) St. Petersburg Math. J. , vol.7 , pp. 681-748
  • 34
    • 0040335157 scopus 로고    scopus 로고
    • English transl. St. Petersburg Math. J. 7 (1996) 681-748.)
    • (1996) St. Petersburg Math. J. , vol.7 , pp. 681-748
  • 35
    • 0013143625 scopus 로고    scopus 로고
    • The polynomial property of self-adjoint elliptic boundary-value problems and the algebraic description of their attributes
    • S.A. Nazarov, The polynomial property of self-adjoint elliptic boundary-value problems and the algebraic description of their attributes. Uspehi Mat. Nauk. 54 (1999) 77-142.
    • (1999) Uspehi Mat. Nauk. , vol.54 , pp. 77-142
    • Nazarov, S.A.1
  • 36
    • 0033262908 scopus 로고    scopus 로고
    • English transl. Russ. Math. Surveys. 54 (1999) 947-1014.)
    • (1999) Russ. Math. Surveys. , vol.54 , pp. 947-1014
  • 37
    • 0009958738 scopus 로고    scopus 로고
    • Weighted spaces with detached asymptotics in application to the Navier-Stokes equations
    • Paseky, Czech. Republic. Springer-Verlag, Berlin (2000)
    • S.A. Nazarov, Weighted spaces with detached asymptotics in application to the Navier-Stokes equations. in: Advances in Mathematical Fluid Mechanics. Paseky, Czech. Republic (1999) 159-191. Springer-Verlag, Berlin (2000).
    • (1999) Advances in Mathematical Fluid Mechanics , pp. 159-191
    • Nazarov, S.A.1
  • 38
    • 0001052403 scopus 로고    scopus 로고
    • The Navier-Stokes problem in a two-dimensional domain with angular outlets to infinity
    • S.A. Nazarov, The Navier-Stokes problem in a two-dimensional domain with angular outlets to infinity. Zap. Nauchn. Sem. St.-Petersburg Otdel. Mat. Inst. Steklov 257 (1999) 207-227.
    • (1999) Zap. Nauchn. Sem. St.-Petersburg Otdel. Mat. Inst. Steklov , vol.257 , pp. 207-227
    • Nazarov, S.A.1
  • 39
    • 28344438339 scopus 로고    scopus 로고
    • English transl. J. Math. Sci. 108 (2002) 790-805.)
    • (2002) J. Math. Sci. , vol.108 , pp. 790-805
  • 40
    • 53649103677 scopus 로고    scopus 로고
    • The spectrum of the elasticity problem for a spiked body
    • S.A. Nazarov, The spectrum of the elasticity problem for a spiked body. Sibirsk. Mat. Zh. 49 (2008) 1105-1127.
    • (2008) Sibirsk. Mat. Zh. , vol.49 , pp. 1105-1127
    • Nazarov, S.A.1
  • 41
    • 53649103677 scopus 로고    scopus 로고
    • (English transl. Siberian Math. J. 49 (2008) 874-893.)
    • (2008) Siberian Math. J. , vol.49 , pp. 874-893
  • 42
    • 70349958879 scopus 로고    scopus 로고
    • On the spectrum of the Steklov problem in peak-shaped domains
    • S.A. Nazarov, On the spectrum of the Steklov problem in peak-shaped domains. Trudy St.-Petersburg Mat. Obshch. 14 (2008) 103-168.
    • (2008) Trudy St.-Petersburg Mat. Obshch. , vol.14 , pp. 103-168
    • Nazarov, S.A.1
  • 44
    • 77950281807 scopus 로고    scopus 로고
    • On the essential spectrum of boundary value problems for systems of differential equations in a bounded peak-shaped domain
    • S.A. Nazarov. On the essential spectrum of boundary value problems for systems of differential equations in a bounded peak-shaped domain. Funkt. Anal. i Prilozhen. 43 (2009) 55-67.
    • (2009) Funkt. Anal. i Prilozhen. , vol.43 , pp. 55-67
    • Nazarov, S.A.1
  • 45
    • 80051973453 scopus 로고    scopus 로고
    • English transl. Funct. Anal. Appl. 43 (2009).)
    • (2009) Funct. Anal. Appl. , vol.43
  • 46
    • 0034563816 scopus 로고    scopus 로고
    • On steady Stokes and Navier-Stokes problems with zero velocity at infinity in a three-dimensional exterior domain
    • S.A. Nazarov and K. Pileckas, On steady Stokes and Navier-Stokes problems with zero velocity at infinity in a three-dimensional exterior domain. Journal of Mathematics of Kyoto University 40 (2000) 475-49.
    • (2000) Journal of Mathematics of Kyoto University , vol.40 , pp. 475-449
    • Nazarov, S.A.1    Pileckas, K.2
  • 47
    • 0010969483 scopus 로고
    • Radiation principles for self-adjoint elliptic problems
    • Leningrad: Leningrad Univ. (Russian)
    • S.A. Nazarov and B.A. Plamenevskii, Radiation principles for self-adjoint elliptic problems. Probl. Mat. Fiz. 13. 192-244. Leningrad: Leningrad Univ. 1991 (Russian).
    • (1991) Probl. Mat. Fiz. , vol.13 , pp. 192-244
    • Nazarov, S.A.1    Plamenevskii, B.A.2
  • 49
    • 0027659065 scopus 로고
    • Asymptotic behavior of the stress-strain state near a spatial singularity of the boundary of the beak tip type
    • S.A. Nazarov and O.R. Polyakova, Asymptotic behavior of the stress-strain state near a spatial singularity of the boundary of the beak tip type. Prikl. Mat. Mekh. 57 (1993) 130-149.
    • (1993) Prikl. Mat. Mekh. , vol.57 , pp. 130-149
    • Nazarov, S.A.1    Polyakova, O.R.2
  • 50
    • 44949267400 scopus 로고
    • (English transl. J. Appl. Math. Mech. 57 (1993) 887-902.)
    • (1993) J. Appl. Math. Mech. , vol.57 , pp. 887-902
  • 51
    • 84858285989 scopus 로고    scopus 로고
    • On the spectrum of the Steklov problem in a domain with a peak
    • S.A. Nazarov and S.A. Taskinen, On the spectrum of the Steklov problem in a domain with a peak. Vestnik St. Petersburg Univ. Math. 41 (2008) 45-52.
    • (2008) Vestnik St. Petersburg Univ. Math. , vol.41 , pp. 45-52
    • Nazarov, S.A.1    Taskinen, S.A.2
  • 52
    • 79955797530 scopus 로고    scopus 로고
    • On essential and continuous spectra of the linearized water-wave problem in a finite pond
    • S.A. Nazarov and J. Taskinen, On essential and continuous spectra of the linearized water-wave problem in a finite pond. Math. Scand. 106 (2009) 1-20.
    • (2009) Math. Scand. , vol.106 , pp. 1-20
    • Nazarov, S.A.1    Taskinen, J.2
  • 53
    • 84980079179 scopus 로고
    • Another approach to elliptic boundary problems
    • J. Peetre, Another approach to elliptic boundary problems. Comm. Pure. Appl. Math. 14 (1961) 711-731.
    • (1961) Comm. Pure. Appl. Math. , vol.14 , pp. 711-731
    • Peetre, J.1
  • 54
    • 0009224702 scopus 로고
    • The asymptotic behavior of the solutions of quasielliptic differential equations with operator coefficients
    • (Russian)
    • B.A. Plamenevskii, The asymptotic behavior of the solutions of quasielliptic differential equations with operator coefficients. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 1332-1375.
    • (1973) Izv. Akad. Nauk SSSR Ser. Mat. , vol.37 , pp. 1332-1375
    • Plamenevskii, B.A.1
  • 56
    • 0001732548 scopus 로고
    • Trapping modes in the theory of surface waves
    • F. Ursell, Trapping modes in the theory of surface waves. Proc. Camb. Phil. Soc. 47 (1951) 347-358.
    • (1951) Proc. Camb. Phil. Soc. , vol.47 , pp. 347-358
    • Ursell, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.