Journal of Mathematical Sciences

, Volume 150, Issue 1, pp 1860–1868 | Cite as

On uniqueness of a solution to the plane problem on interaction of surface waves with obstacle



We consider the plane linear boundary value problem describing the behavior of time-harmonic water waves with an obstacle formed by partially and totally immersed bodies of infinite length and also by the part of bottom the topography of which is different from that in the plane case. We study a special two-dimensional case where the crests of waves incoming on the obstacle are parallel to the obstacle generators. Bibliography: 10 titles.


Conformal Mapping Integral Identity Plane Case Homogeneous Problem Uniqueness Criterion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. G. Kuznetsov, “Nodal lines and uniqueness of solutions to linear water-wave problems” [in Russian], Tr. S. Peterb. Mat. O-va 13 (2007), 73–91; English transl.: Am. Math. Soc., Providence, 2008.Google Scholar
  2. 2.
    M. McIver, “An example of non-uniqueness in the two-dimensional linear water-wave problem,” J. Fluid Mech. 315 (1996), 257–266.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    F. John, “On the motion of floating bodies. II,” Comm. Pure Appl. Math. 3 (1950), 45–101.CrossRefMathSciNetGoogle Scholar
  4. 4.
    M. J. Simon and F. Ursell, “Uniqueness in linearized two-dimensional water-wave problems,” J. Fluid Mech. 148 (1984), 137–154.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    N. Kuznetsov, “Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary angles,” C. R. Mecanique 332 (2004), 73–78.CrossRefGoogle Scholar
  6. 6.
    B. R. Vainberg and V. G. Maz’ya, On the problem of the steady-state oscillations of a fluid layer of variable depth [in Russian], Tr. Mosk. Mat. O-va 28 (1973), 57–74.Google Scholar
  7. 7.
    N. Kuznetsov, V. Maz’ya, and B. Vainberg, Linear Water Waves: A Mathematical Approach, Cambridge Univ. Press, Cambridge, 2002.MATHGoogle Scholar
  8. 8.
    P. H. Moon and D. E. Spencer, Field Theory Handbook. Including Coordinate Systems, Differential Equations and Their Solutions, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1988.Google Scholar
  9. 9.
    Ph. M. Morse and H. Feshbach, Methods of Theoretical Physics, II, McGraw-Hill Book Co., New York, 1953.MATHGoogle Scholar
  10. 10.
    S. A. Nazarov and B. A. Plamenevskii, Elliptic Problems in Domains with Piecewise Smooth Boundary [in Russian], Nauka, Moscow, 1991.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of Problems of Mechanical Engineering RASSt. PetersburgRussia

Personalised recommendations