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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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