Abstract
The behavior of the solution of a boundary value problem for a parabolic equation with rapidly oscillating coefficientsɛ −1 x,ɛ −2k t), (k⋝0) in a perforated domain for ε→0 is studied. Some estimates of the deviation of the solution and energy for the original boundary value problem from the solution and energy of the corresponding homogenized problem are found. In this investigation methods developed by Oleinik, Zhikov, Kozlov, Bensoussan, Lions, Papanikolaou, Cioranescu, and Paulin are used. Bibliography: 15 titles.
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 17, pp. 27–50, 1994.
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Shaposhnikova, T. On the covergence of solutions of parabolic equations with rapidly oscillating coefficients in perforated domains. J Math Sci 75, 1631–1645 (1995). https://doi.org/10.1007/BF02368667
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DOI: https://doi.org/10.1007/BF02368667