RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 Mat. Sb., 2008, Volume 199, Number 12, Pages 53–78 (Mi msb3939)

Concentration of trapped modes in problems of the linearized theory of water waves

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

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 $h\in(0,h(d,N)]$ 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.

DOI: https://doi.org/10.4213/sm3939

Full text: PDF file (734 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:12, 1783–1807

Bibliographic databases:

UDC: 517.958:531.327
MSC: Primary 76B15; Secondary 35Q35

Citation: S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Mat. Sb., 199:12 (2008), 53–78; Sb. Math., 199:12 (2008), 1783–1807

Citation in format AMSBIB
\Bibitem{Naz08} \by S.~A.~Nazarov \paper Concentration of trapped modes in problems of the linearized theory of water waves \jour Mat. Sb. \yr 2008 \vol 199 \issue 12 \pages 53--78 \mathnet{http://mi.mathnet.ru/msb3939} \crossref{https://doi.org/10.4213/sm3939} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2489688} \zmath{https://zbmath.org/?q=an:1157.76006} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2008SbMat.199.1783N} \elib{http://elibrary.ru/item.asp?id=20359297} \transl \jour Sb. Math. \yr 2008 \vol 199 \issue 12 \pages 1783--1807 \crossref{https://doi.org/10.1070/SM2008v199n12ABEH003981} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000264258100009} \elib{http://elibrary.ru/item.asp?id=13570984} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-66149116451} 

• http://mi.mathnet.ru/eng/msb3939
• https://doi.org/10.4213/sm3939
• http://mi.mathnet.ru/eng/msb/v199/i12/p53

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. A. Nazarov, “Simple method for finding trapped modes in problems of the linear theory of surface waves”, Dokl. Math., 80:3 (2009), 914–917
2. Nazarov S.A., Videman J.H., “A sufficient condition for the existence of trapped modes for oblique waves in a two-layer fluid”, Proc. R. Soc. A, 465:2112 (2009), 3799–3816
3. Nazarov S.A., “A novel approach for detecting trapped surface waves in a canal with periodic underwater topography”, Comptes Rendus Mécanique, 337:8 (2009), 610–615
4. S. A. Nazarov, “Sufficient conditions of the existence of trapped modes in problems of the linear theory of surface waves”, J. Math. Sci. (N. Y.), 167:5 (2010), 713–725
5. S. A. Nazarov, “The point spectrum of water-wave problem in intersecting canals”, J. Math. Sci. (N. Y.), 175:6 (2011), 685–697
6. S. A. Nazarov, “On the asymptotics of an eigenvalue of a waveguide with thin shielding obstacle and Wood's anomalies”, J. Math. Sci. (N. Y.), 178:3 (2011), 292–312
7. Cardone G., Durante T., Nazarov S.A., “Water-waves modes trapped in a canal by a near-surface rough body”, ZAMM Z. Angew. Math. Mech., 90:12 (2010), 983–1004
8. Nazarov S.A., Videman J.H., “Existence of edge waves along three-dimensional periodic structures”, J. Fluid Mech., 659 (2010), 225–246
9. S. A. Nazarov, “Formation of gaps in the spectrum of the problem of waves on the surface of a periodic channel”, Comput. Math. Math. Phys., 50:6 (2010), 1038–1054
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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
16. S. A. Nazarov, “Concentration of frequencies of trapped waves in problems on freely floating bodies”, Sb. Math., 203:9 (2012), 1269–1294
17. 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
18. 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
19. 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
20. 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
21. Nazarov S.A., Taskinen J., Videman J.H., “Asymptotic Behavior of Trapped Modes in Two-Layer Fluids”, Wave Motion, 50:2 (2013), 111–126
22. 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
23. 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
24. 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
25. S. A. Nazarov, “Asymptotic expansions of eigenvalues of the Steklov problem in singularly perturbed domains”, St. Petersburg Math. J., 26:2 (2015), 273–318
26. 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
27. 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
•  Number of views: This page: 729 Full text: 62 References: 83 First page: 13