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Exact solution of one boundary-value problem

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Abstract

We study the boundary-value perlodic problem u tt −u xx =F(x, t), u(0, t)=u(π, t)=0, u(x, t+T)=u(x, t), (x, t) ∈ R 2. By using the Vejvoda-Shtedry operator, we determine a solution of this problem.

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References

  1. Yu. A. Mitropol'skii, G. P. Khoma, and M. I. Gromyak, Asymptotic Methods of Sutdy for Quasilinear 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 connection between the numbertheoretic character of the period and geometric properties of solutions,” Differents. Uravn., 20, No. 10, 1733–1739 (1984).

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Authors
  1. A. O. Botyuk
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Additional information

Ternopol Pedagogical Institute, Temopol. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7, pp. 998–1001, July, 1997.

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Botyuk, A.O. Exact solution of one boundary-value problem. Ukr Math J 49, 1120–1124 (1997). https://doi.org/10.1007/BF02528758

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  • DOI: https://doi.org/10.1007/BF02528758

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