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Nonlocal boundary-value problem for parabolic equations

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Abstract

We study the problem for Shilov parabolic equations of arbitrary order with constant coefficients with conditions nonlocal in time and periodic in space variables. We establish conditions for the existence and uniqueness of a classical solution of the problem and prove metric theorems on lower bounds of small denominators appearing in the construction of a solution of the problem.

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Authors and Affiliations

  1. Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'vov

    N. M. Zadorozhna & B. I. Ptashnik

  2. Kamenets-Podol'sk Agriculture Institute, Kamenets-Podol'sk

    O. M. Mel'nik

Authors
  1. N. M. Zadorozhna
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  2. O. M. Mel'nik
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  3. B. I. Ptashnik
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1621–1626, December, 1994.

The work was supported by the Foundation for Fundamental Studies of Ukrainian State Committee on Science and Technology.

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Zadorozhna, N.M., Mel'nik, O.M. & Ptashnik, B.I. Nonlocal boundary-value problem for parabolic equations. Ukr Math J 46, 1795–1802 (1994). https://doi.org/10.1007/BF01063168

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  • DOI: https://doi.org/10.1007/BF01063168

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