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Asymptotics of a solution of a discontinuous singularly perturbed Cauchy problem

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Abstract

We construct the asymptotic expansion of a solution of the Cauchy problem for a singularly perturbed system of differential equations whose right-hand side is discontinuous on a certain surface. We consider the case where the surface of discontinuity is crossed and estimate the remainder of the constructed asymptotic expansion.

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References

  1. Yu. A. Mitropol'skii and A. M. Samoilenko, “On asymptotic expansions in nonlinear mechanics,”Ukr. Mat. Zh.,31, No. 1, 42–53 (1979).

    Google Scholar 

  2. A. N. Tikhonov, “Methods of small parameter and their applications,”Differents. Uravn.,21, No. 10, 1659–1661 (1985).

    Google Scholar 

  3. M. G. Dmitriev,Singular Perturbations in Problems of Optimal Control [in Russian], Doctor Degree Thesis (Physics and Mathematics), Krasnoyarsk (1983).

  4. V. G. Sushko, “Asymptotic expansion of the solution of a differential equation with discontinuous coefficients in small parameter,”Vestn. Mosk. Univ., Vychisl. Mat., Kibernet., No. 3, 3–8 (1983).

    Google Scholar 

  5. A. F. Filippov,Differential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  6. V. I. Utkin,Sliding Modes in Problems of Optimization and Control [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  7. A. B. Vasil'eva and V. F. Butuzov,Asymptotic Expansions of Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow.

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Authors and Affiliations

  1. Odessa Institute of Civil Engineers, Odessa

    T. A. Mel'nik

Authors
  1. T. A. Mel'nik
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1502–1508, November, 1994.

The present work was supported by the Ukrainian State Committee on Science and Technology.

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Mel'nik, T.A. Asymptotics of a solution of a discontinuous singularly perturbed Cauchy problem. Ukr Math J 46, 1660–1666 (1994). https://doi.org/10.1007/BF01058884

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  • DOI: https://doi.org/10.1007/BF01058884

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