Asymptotic analysis of a parabolic semilinear problem with nonlinear boundary multiphase interactions in a perforated domain |
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Authors: | T A Mel’nik O A Sivak |
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Institution: | 1.National Taras Shevchenko,University of Kyiv,Kyiv,Ukraine |
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Abstract: | We consider a parabolic semilinear problem with rapidly oscillating coefficients in a domain Ωε that is ε-periodically perforated by small holes of size O\mathcal {O}(ε). The holes are divided into two ε-periodical sets depending on the boundary interaction at their surfaces, and two different
nonlinear Robin boundary conditions σε(u
ε) + εκ
m
(u
ε) = εg
(m)
ε, m = 1, 2, are imposed on the boundaries of holes. We study the asymptotics as ε → 0 and establish a convergence theorem without
using extension operators. An asymptotic approximation of the solution and the corresponding error estimate are also obtained.
Bibliography: 60 titles. Illustrations: 1 figure. |
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Keywords: | |
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