Abstract
The behavior of the remainder term of the asymptotic expansion for solutions of a quasi-linear parabolic Cauchy-Dirichlet problem in a sequence of domains with fine-granulated boundary is studied. By using a modification of the asymptotic expansion and new pointwise estimates of solutions of the model problem, the uniform convergence of the remainder term to zero is proved.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 53, Suzdal Conference-2006, Part 1, 2008.
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Zhuravskaya, A.V. Nonlinear parabolic problems in perforated domains. J Math Sci 157, 491–495 (2009). https://doi.org/10.1007/s10958-009-9329-y
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DOI: https://doi.org/10.1007/s10958-009-9329-y