Abstract
For a nonautonomous wave equation with homogeneous boundary conditions, we construct one-frequency approximations of asymptotic solutions by using periodic Ateb-functions. Resonance and nonresonance cases are considered.
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References
A. D. Myshkis and A. M. Filimonov, “Periodic oscillations in nonlinear one-dimensional continua,” in:International Conference on Nonlinear Oscillations [in Russian], Vol. 1, Naukova Dumka, Kiev (1984), pp. 274–276.
P. M. Senik, “Inversions of incomplete Beta-function,”Ukr. Mat. Zh.,21, No. 3, 325–333 (1968).
B. I. Sokil and A. F. Barvinskii, “On the asymptotic solution of one nonlinear boundary-value problem,”Dokl. Akad. Nauk Ukr. SSR. Ser. A, No. 1, 22–26 (1980).
N. N. Moiseev,Asymptotic Methods in Nonlinear Mechanics [in Russian], Nauka, Moscow (1969).
Yu. A. Mitropol'skii and B. I. Moseenkov,Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kiev (1976).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1714–1716, December, 1995.
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Sokil, B.I. On the construction of asymptotic approximations for a nonautonomous wave equation. Ukr Math J 47, 1960–1963 (1995). https://doi.org/10.1007/BF01060972
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DOI: https://doi.org/10.1007/BF01060972