Solution of a Nonlinear Thermal Problem in Connected Domains

Abstract

In this paper, the limit behavior of nonlinear problems with nonhomogeneous Fourier boundary conditions, in a connected domain is established. This domain consists of two separate parts jointed by a set of bridges. The parameter describing the heterogeneities of the material and the size of the bridges can be very small. The homogenization method is used to estimate the field of temperatures attainable in the medium, depending of the relative order of the size of the bridges. Three situations are studied according to the connectedness of the components of the domain.