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Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain

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Abstract

We establish the convergence of the Rothe method for a parabolic equation with nonlocal boundary conditions and obtain an a priori estimate for the constructed difference scheme in the grid norm on a ball. We prove that the suggested iterative process for the solution of the posed problem converges in the small.

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Authors and Affiliations

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

    Yu. A. Mitropol’skii

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

    A. A. Berezovskii

  3. Kabardino-Balkarian University, Nalchik

    M. Kh. Shkhanukov-Lafishev

Authors
  1. Yu. A. Mitropol’skii
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  2. A. A. Berezovskii
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  3. M. Kh. Shkhanukov-Lafishev
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 244–254, February, 1997.

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Mitropol’skii, Y.A., Berezovskii, A.A. & Shkhanukov-Lafishev, M.K. Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain. Ukr Math J 49, 269–280 (1997). https://doi.org/10.1007/BF02486441

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  • DOI: https://doi.org/10.1007/BF02486441

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