| Title:
|
Water-wave problem for a vertical shell (English) |
| Author:
|
Kuznetsov, Nikolay |
| Author:
|
Maz'ya, Vladimir |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
411-420 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for finding a solution. (English) |
| Keyword:
|
time-harmonic velocity potential |
| Keyword:
|
uniqueness theorem |
| Keyword:
|
Helmholtz equation |
| Keyword:
|
Neumann’s eigenvalue problem for Laplacian |
| Keyword:
|
integral equation method |
| Keyword:
|
weighted Hölder spaces |
| Keyword:
|
velocity potential |
| Keyword:
|
uniqueness |
| Keyword:
|
Neumann’s eigenvalue problem |
| Keyword:
|
Laplacian |
| Keyword:
|
linearized problem |
| Keyword:
|
radiation |
| Keyword:
|
scattering |
| Keyword:
|
time-harmonic water wave |
| Keyword:
|
vertical shell |
| MSC:
|
35Q35 |
| MSC:
|
76B15 |
| MSC:
|
76M25 |
| idZBL:
|
Zbl 1011.76011 |
| idMR:
|
MR1844279 |
| DOI:
|
10.21136/MB.2001.134028 |
| . |
| Date available:
|
2009-09-24T21:52:09Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134028 |
| . |
| Reference:
|
[1] C. J. R. Garrett: Bottomless harbours.J. Fluid Mech. 43 (1970), 433–449. Zbl 0212.60101, 10.1017/S0022112070002495 |
| Reference:
|
[2] A. Hulme: Some applications of Maz’ja’s uniqueness theorem to a class of linear water wave problems.Math. Proc. Camb. Phil. Soc. 95 (1984), 511–519. Zbl 0546.76031, MR 0727091, 10.1017/S0305004100061417 |
| Reference:
|
[3] F. John: On the motion of floating bodies, II.Comm. Pure Appl. Math. 3 (1950), 45–101. MR 0037118, 10.1002/cpa.3160030106 |
| Reference:
|
[4] N. G. Kuznetsov: Plane problem of the steady-state oscillations of a fluid in the presence of two semiimmersed cylinders.Math. Notes Acad. Sci. USSR 44 (1988), 685–690. MR 0972199 |
| Reference:
|
[5] N. G. Kuznetsov: Uniqueness of a solution of a linear problem for stationary oscillations of a liquid.Diff. Equations 27 (1991), 187–194. Zbl 0850.76059, MR 1109387 |
| Reference:
|
[6] N. Kuznetsov, P. McIver: On uniqueness and trapped modes in the water-wave problem for a surface-piercing axisymmetric body.Q. J. Mech. Appl. Math. 50 (1997), 565–580. MR 1488385, 10.1093/qjmam/50.4.565 |
| Reference:
|
[7] M. J. Lighthill: Two-dimensional analyses related to wave-energy extraction by submerged resonant ducts.J. Fluid Mech. 91 (1979), 253–317. Zbl 0403.76025, 10.1017/S0022112079000148 |
| Reference:
|
[8] V. G. Maz’ya: Solvability of the problem on the oscillations of a fluid containing a submerged body.J. Soviet Math. 10 (1978), 86–89. 10.1007/BF01109726 |
| Reference:
|
[9] V. G. Maz’ya: Boundary integral equations.Encyclopaedia of Math. Sciences 27 (1991), 127–222. MR 1098507, 10.1007/978-3-642-58175-5_2 |
| Reference:
|
[10] V. G. Maz’ya, B. A. Plamenevskii: Schauder estimates of solutions of elliptic boundary value problems in domains with edges on the boundary.Elliptic boundary value problems AMS Transl. 123 (1984), 141–169. |
| Reference:
|
[11] V. G. Maz’ya, J. Rossmann: Über die Asymptotic der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten.Math. Nachr. 138 (1988), 27–53. MR 0975198, 10.1002/mana.19881380103 |
| Reference:
|
[12] M. McIver: An example of non-uniqueness in the two-dimensional linear water-wave problem.J. Fluid Mech. 315 (1996), 257–266. Zbl 0869.76010, MR 1403701, 10.1017/S0022112096002418 |
| Reference:
|
[13] P. McIver, M. McIver: Trapped modes in an axisymmetric water-wave problem.Q. J. Mech. Appl. Math. 50 (1997), 165–178. MR 1451065, 10.1093/qjmam/50.2.165 |
| Reference:
|
[14] M. J. Simon: Wave-energy extraction by a submerged cylindrical resonant duct.J. Fluid Mech. 104 (1981), 159–187. Zbl 0463.76021, 10.1017/S0022112081002875 |
| Reference:
|
[15] M. J. Simon, N. G. Kuznetsov: On uniqueness of the water-wave problem for a floating toroidal body.Appl. Math. Report 96/1 (1996), Department of Mathematics, University of Manchester, England. |
| Reference:
|
[16] M. J. Simon, F. Ursell: Uniqueness in linearized two-dimensional water-wave problem.J. Fluid Mech. 148 (1984), 137–154. MR 0778139, 10.1017/S0022112084002287 |
| Reference:
|
[17] J. R. Thomas: The absorption of wave energy by a three-dimensional submerged duct.J. Fluid Mech. 104 (1981), 189–215. Zbl 0455.76007, 10.1017/S0022112081002887 |
| Reference:
|
[18] F. Ursell: Surface waves on deep water in the presence of a submerged circular cylinder, I.Proc. Camb. Phil. Soc. 46 (1950), 141–152. Zbl 0035.42201, MR 0033714, 10.1017/S0305004100025561 |
| Reference:
|
[19] F. Ursell: Some unsolved and unfinished problems in the theory of waves.Wave Asymptotics, Camb. Univ. Press, Cambridge, 1992. Zbl 0817.76008, MR 1174354 |
| Reference:
|
[20] B. R. Vainberg, V. G. Maz’ya: On the problem of the steady state oscillations of a fluid layer of variable depth.Trans. Moscow Math. Soc. 28 (1973), 56–73. MR 0481654 |
| . |
