Abstract
By using a nonlinear boundary-value problem for a second-order hyperbolic equation as an example, we justify a new approach to the application of the Krylov —Bogolyubov —Mitropol'skii asymptotic methods. For certain linear problems, we present compatibility conditions and relations that enable one to construct the exact solutions of these problems.
References
N. N. Bogolyubov and Yu. A. Mitropol'skii,Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).
Yu. A. Mitropol'skii,Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).
Yu. A. Mitropol'skii and B. I. Moseenkov,Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kiev (1976).
Yu. A. Mitropol'skii and G. P. Khoma,Mathematical Justification of Asymptotic Methods in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1983).
Yu. A. Mitropol'skii and L. G. Khoma, “Existence of the classical solution of a mixed problem for a second-order linear hyperbolic equation,”Ukr. Mat. Zh.,45, No. 9, 1232–1239 (1993).
A. N. Tikhonov and A. A. Samarskii,Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977).
V. A. Chernyatin,Justification of the Fourier Method in the Mixed Problem for Partial Differential Equations [in Russian], Moscow University, Moscow (1991).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 468–470, April, 1994.
Rights and permissions
About this article
Cite this article
Khoma, L.G. Application of existence theorems to asymptotic decompositions. Ukr Math J 46, 499–501 (1994). https://doi.org/10.1007/BF01060425
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01060425