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

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    I. A. Lukovskii & A. N. Timokha

Authors
  1. I. A. Lukovskii
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  2. A. N. Timokha
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1642–1652, December, 1993.

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Lukovskii, I.A., Timokha, A.N. Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields. Ukr Math J 45, 1849–1860 (1993). https://doi.org/10.1007/BF01061355

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  • DOI: https://doi.org/10.1007/BF01061355

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