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 Ωe that is e-periodically perforated by small holes of size $\mathcal {O}$ (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 σe(u e) + eκ m (u e) = eg (m) e, m = 1, 2, are imposed on the boundaries of holes. We study the asymptotics as e → 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.