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A periodic problem for the inhomogeneous equation of string oscillations

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Ukrainian Mathematical Journal Aims and scope

Abstract

We study a periodic problem for the equation u tt−uxx=g(x, t), u(x, t+T)=u(x, t), u(x+ω, t)= =u(x, t), ℝ2 and establish conditions of the existence and uniqueness of the classical solution.

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References

  1. Yu. A. Mitropol’skii, G. P. Khoma, and M. I. Gromyak, Asymptotic Methods for the Investigation of Quasiwave Equations of Hyperbolic Type [in Russian], Naukova Dumka, Kiev (1991).

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  2. O. Vejvoda, and M. Shtedry, “The existence of classical periodic solutions of the wave equation: A relation between the number-theoretic character of the period and geometric properties of solutions”, Differents. Uravn., 20, No. 10, 1733–1739 (1984).

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Authors and Affiliations

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

    Yu. A. Mitropol’skii

  2. Ternopol Pedagogical Institute, USSR

    G. P. Khoma & P. V. Tsynaiko

Authors
  1. Yu. A. Mitropol’skii
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  2. G. P. Khoma
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  3. P. V. Tsynaiko
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 558–565, April, 1997.

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Mitropol’skii, Y.A., Khoma, G.P. & Tsynaiko, P.V. A periodic problem for the inhomogeneous equation of string oscillations. Ukr Math J 49, 618–627 (1997). https://doi.org/10.1007/BF02487325

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  • DOI: https://doi.org/10.1007/BF02487325

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