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Nonlocal boundary-value problem for parabolic equations with variable coefficients

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Abstract

We study the boundary-value problem for Petrovskii parabolic equations of arbitrary order with variable coefficients with conditions nonlocal in time. We establish conditions for the existence and uniqueness of a classical solution of this 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, Lvov

    N. M. Zadorozhna & B. I. Ptashnyk

Authors
  1. N. M. Zadorozhna
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  2. B. I. Ptashnyk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 7, pp. 915–921, July, 1995.

This work was partially supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology.

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Zadorozhna, N.M., Ptashnyk, B.I. Nonlocal boundary-value problem for parabolic equations with variable coefficients. Ukr Math J 47, 1050–1057 (1995). https://doi.org/10.1007/BF01084900

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  • DOI: https://doi.org/10.1007/BF01084900

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