Abstract:
Problems of the linearized theory of waves on the surface of an ideal fluid filling a half-space or an infinite 3D-canyon are considered. Families of submerged or surface-piercing bodies parametrized by a characteristic
linear size h>0 are found that have the following property: for each d>0 and each positive integer
N there exists h(d,N)>0 such that for h∈(0,h(d,N)] the interval [0,d] of the continuous spectrum of the corresponding problem contains at least N eigenvalues corresponding to trapped modes, that is, to solutions of the homogeneous problem that decay exponentially at infinity and possess finite energy.
Bibliography: 38 titles.
\Bibitem{Naz08}
\by S.~A.~Nazarov
\paper Concentration of trapped modes in problems of the linearized theory of water waves
\jour Sb. Math.
\yr 2008
\vol 199
\issue 12
\pages 1783--1807
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This publication is cited in the following 30 articles:
Sergei A. Nazarov, Keijo M. Ruotsalainen, “Curved channels with constant cross sections may support trapped surface waves”, Z. Angew. Math. Phys., 74:4 (2023)
Filipe S. Cal, Gonçalo A.S. Dias, Bruno M.A.M. Pereira, “Trapped modes in a fluid with three layers topped by a rigid lid”, Math Methods in App Sciences, 45:16 (2022), 9928
S. A. Nazarov, “Modeling of a Singularly Perturbed Spectral Problem by Means of Self-Adjoint Extensions of the Operators of the Limit
Problems”, Funct. Anal. Appl., 49:1 (2015), 25–39
Durante T., “Accumulation Effect For Water-Waves Mode Trapped in a Canal”, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics 2014 (Icnaam-2014), AIP Conference Proceedings, 1648, eds. Simos T., Tsitouras C., Amer Inst Physics, 2015, UNSP 390007
S. A. Nazarov, “Asymptotic expansions of eigenvalues of the Steklov problem in singularly perturbed domains”, St. Petersburg Math. J., 26:2 (2015), 273–318
Piat V.Ch., Nazarov S.A., Ruotsalainen K., “Spectral gaps for water waves above a corrugated bottom”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 469:2149 (2013), 20120545
Nazarov S.A., Taskinen J., Videman J.H., “Asymptotic Behavior of Trapped Modes in Two-Layer Fluids”, Wave Motion, 50:2 (2013), 111–126
Nazarov S.A., Taskinen J., “Localization Estimates for Eigenfrequencies of Waves Trapped by a Freely Floating Body in a Channel”, SIAM J. Math. Anal., 45:4 (2013), 2523–2545
Kamotski I., Mazya V., “Estimate for a Solution to the Water Wave Problem in the Presence of a Submerged Body”, Russ. J. Math. Phys., 20:4 (2013), 453–467
Nazarov S.A., Taskinen J., “Properties of the Spectrum in the John Problem on a Freely Floating Submerged Body in a Finite Basin”, Differ. Equ., 49:12 (2013), 1544–1559
S. A. Nazarov, “Concentration of frequencies of trapped waves in problems on freely floating bodies”, Sb. Math., 203:9 (2012), 1269–1294
S. A. Nazarov, “Asymptotic behavior of the eigenvalues of the Steklov problem on a junction of domains of different limiting dimensions”, Comput. Math. Math. Phys., 52:11 (2012), 1574–1589
Cal F.S., Dias G.S.A., Videman J.H., “Existence of trapped modes along periodic structures in a two-layer fluid”, Quart. J. Mech. Appl. Math., 65:2 (2012), 273–292
Kamotski I.V. Maz'ya V.G., “On the linear water wave problem in the presence of a critically submerged body”, SIAM J. Math. Anal., 44:6 (2012), 4222–4249
S. A. Nazarov, “Localization of surface waves by small perturbations of the boundary of a semisubmerged body”, J. Appl. Industr. Math., 6:2 (2012), 216–223
Nazarov S.A., “Incomplete comparison principle in problems about surface waves trapped by fixed and freely floating bodies”, J. Math. Sci., 175:3 (2011), 309–348
J. H. Videman, V. Chiado' Piat, S. A. Nazarov, “Asymptotics of frequency of a surface wave trapped by a slightly inclined barrier in a liquid layer”, J. Math. Sci. (N. Y.), 185:4 (2012), 536–553
S. A. Nazarov, J. Taskinen, “Double-sided estimates for eigenfrequencies in the John problem for freely floating body”, J. Math. Sci. (N. Y.), 185:5 (2012), 707–720
Nazarov S.A., Videman J.H., “Trapping of water waves by freely floating structures in a channel”, Proc. R. Soc. A, 467:2136 (2011), 3613–3632
Nazarov S.A., “A body traps as many water-wave modes in a symmetric channel as it wishes”, Russ. J. Math. Phys., 18:2 (2011), 183–194
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