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.
References
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).
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).
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