Abstract
We investigate the behavior of a remainder of an asymptotic expansion for solutions of a quasi-linear parabolic Cauchy-Dirichlet problem in a sequence of domains with fine-grained boundary. By using a modification of an asymptotic expansion and new pointwise estimates for a solution of a model problem, we prove the uniform convergence of the remainder to zero.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1244–1258, September, 2004.
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Skrypnik, I.V., Zhuravskaya, A.V. Uniform approximation of solutions of nonlinear parabolic problems in perforated domains. Ukr Math J 56, 1481–1498 (2004). https://doi.org/10.1007/s11253-005-0128-4
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DOI: https://doi.org/10.1007/s11253-005-0128-4