On homogenization of the mixed boundary-value problem for the heat equation in a domain whose part contains channels arranged in a periodic way

Abstract

In this paper, we study the asymptotic behavior of the solutionsue (e is a small parameter) of boundaryvalue problems for the heat equation in the domain Ωe=Ω−∪Ωe+∪γ one part of which (Ωe+) contains e-periodically situated channels with diameters of order e and the other part of which (Ω+) is a homogeneous medium; γ=∂Ωe+∩∂Ω+. On the boundary of the channels the Neumann boundary condition is posed, and on ∂Ωe∩∂Ω the Dirichlet boundary condition is prescribed. The homogenized problem is the Dirichlet problem in Ω with the transmission condition on γ. The estimates for the difference betweenue and the solution of the homogenized problem are obtained. Bibliography: 14 titles.