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Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1849–1860 | Cite as

Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields

  • I. A. Lukovskii
  • A. N. Timokha
Article

Abstract

Variational problems equivalent to nonlinear evolutionary boundary-value problems with a free boundary are formulated. These problems arise in the theory of interaction of limited volumes of liquid, gas, and their interface with acoustic fields. It is proved that the principle of separation of motions can be applied to these variational problems. The problem of a capillary-acoustic equilibrium form is given in a variational formulation.

Keywords

Surface Wave Free Boundary Variational Problem Variational Formulation Acoustic Field 
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.

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • I. A. Lukovskii
    • 1
  • A. N. Timokha
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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