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A class of boundary value problems in the theory of surface waves

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Abstract

Boundary value problems are formulated concerning characteristic oscillations relative to capillary-sound equilibrium forms and theorems are established concerning properties of spectra of these problems; theorems are also presented concerning stability of the indicated forms of equilibrium.

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Literature cited

  1. G. S. Narimanov, L. V. Dokuchaev, and I. A. Lukovskii, Nonlinear Dynamics of an Aircraft with a Fluid [in Russian], Mashinostroenie, Moscow (1977).

    Google Scholar 

  2. I. T. Selezov, Yu. G. Krivonos, and V. V. Yakovlev, Scattering of Waves by Local Nonhomogeneities in Continuous Media [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  3. I. A. Lukovskii and A. N. Timokha, “On the problem of the control of a free surface of a bounded volume of fluid with the aid of sound,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 52–55 (1989).

    Google Scholar 

  4. I. A. Lukovskii and A. N. Timokha, “Nonlinear dynamics of the surface of separation of a liquid and a gas with a high-frequency acoustic field present in the gas. Stationary regimes of motion,” Inst. Mat., Akad. Nauk Ukr. SSR, Preprint 88.9, Kiev (1988).

    Google Scholar 

  5. I. A. Lukovskii, Introduction to the Nonlinear Dynamics of a Solid Body with Fluid-Containing Cavities [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

  6. I. A. Lukovskii and A. N. Timokha, “On free oscillations of a “fluid-gas” system in a cylindrical container in a weak gravitational field,” in: Direct Methods in Problems of Dynamics and Stability of Multi-Dimensional Systems [in Russian], Inst. Mat., Akad. Nauk Ukr. SSR, Kiev (1986), pp. 5–12.

    Google Scholar 

  7. A. D. Myshkis (ed.), Hydrodynamics of Weightlessness [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  8. J. J. Stoker, Water Waves, Interscience, New York (1957).

    Google Scholar 

  9. I. A. Lukovskii and A. N. Timokha, “Nonlinear dynamics of the surface of separation of a liquid and a gas with a high-frequency acoustic field present in the gas. Stability of stationary regimes,” Inst. Mat., Akad. Nauk Ukr. SSR, Preprint 88.10, Kiev (1988).

    Google Scholar 

  10. I. A. Lukovskii and A. N. Timokha, “Spatial motions of a reservoir with a fluid under the action of a vibro-acoustic load,” Inst. Mat. Akad. Nauk UKr. SSR, Preprint 90.33, Kiev (1990).

    Google Scholar 

  11. I. A. Lukovskii and A. N. Timokha, “On self-adjointness of an integro-differential operator,” Ukr. Mat. Zh.,42, No. 3, 421–423 (1990).

    Google Scholar 

  12. J.-P. Oben, Approximate Solution of Elliptic Boundary Value Problems [Russian translation], Mir, Moscow (1977).

    Google Scholar 

  13. L. A. Lyusternik and V. I. Sobolev, A Short Course of Functional Analysis [in Russian], Vyssh. Shkola, Moscow (1982).

    Google Scholar 

  14. A. N. Komarenko, I. A. Lukovskii, and S. F. Feshchenko, “On a characteristic boundary value problem with a parameter in the boundary conditions,” Ukr. Mat. Zh.,17, No. 6, 22–30 (1965).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 359–364, March, 1991.

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Lukovskii, I.A., Timokha, A.N. A class of boundary value problems in the theory of surface waves. Ukr Math J 43, 322–328 (1991). https://doi.org/10.1007/BF01060842

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  • DOI: https://doi.org/10.1007/BF01060842

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