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On a nonlocal problem for a parabolic equation

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Abstract

We study a nonlocal boundary-value problem for a parabolic equation in a two-dimensional domain, establish ana priori estimate in the energy norm, prove the existence and uniqueness of a generalized solution from the classW 1,02 (Q T ), and construct a difference scheme for the second-order approximation.

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Authors and Affiliations

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

    Yu. A. Mitropol'skii (Academician)

  2. Kabardino-Balkar University, NII PMA, Nalchik

    M. Kh. Shkhanukov

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

    A. A. Berezovskii

Authors
  1. Yu. A. Mitropol'skii
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  2. M. Kh. Shkhanukov
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  3. A. A. Berezovskii
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 790–800, June, 1995.

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Mitropol'skii, Y.A., Shkhanukov, M.K. & Berezovskii, A.A. On a nonlocal problem for a parabolic equation. Ukr Math J 47, 911–923 (1995). https://doi.org/10.1007/BF01058782

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  • DOI: https://doi.org/10.1007/BF01058782

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