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2010
Journal Article
Titel
Asymptotic analysis of a parabolic semilinear problem with nonlinear boundary multiphase interactions in a perforated domain
Abstract
We consider a parabolic semilinear problem with rapidly oscillating coefficients in a domain Oe that is e-periodically perforated by small holes of size O(e). The holes are divided into two e-periodical sets depending on the boundary interaction at their surfaces, and two different nonlinear Robin boundary conditions se(ue) + ekm(ue) = eg(m)e, m = 1, 2, are imposed on the boundaries of holes. We study the asymptotics as e RT 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.