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Application of existence theorems to asymptotic decompositions

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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.

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References

  1. N. N. Bogolyubov and Yu. A. Mitropol'skii,Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).

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  2. Yu. A. Mitropol'skii,Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).

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  3. Yu. A. Mitropol'skii and B. I. Moseenkov,Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kiev (1976).

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  4. Yu. A. Mitropol'skii and G. P. Khoma,Mathematical Justification of Asymptotic Methods in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1983).

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  5. 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).

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  6. A. N. Tikhonov and A. A. Samarskii,Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977).

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  7. V. A. Chernyatin,Justification of the Fourier Method in the Mixed Problem for Partial Differential Equations [in Russian], Moscow University, Moscow (1991).

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Authors and Affiliations

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

    L. G. Khoma

Authors
  1. L. G. Khoma
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 468–470, April, 1994.

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Khoma, L.G. Application of existence theorems to asymptotic decompositions. Ukr Math J 46, 499–501 (1994). https://doi.org/10.1007/BF01060425

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  • DOI: https://doi.org/10.1007/BF01060425

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