Upscaling in nonlinear thermal diffusion problems

The aim of this paper is to study the homogenization of a nonlinear problem arising in the modelling of thermal diffusion in a two-component composite. We consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We assume that we have nonlinear sources and that at the interface between our two materials the flux is continuous and depends in a nonlinear way on the jump of the temperature field. We shall be interested in describing the asymptotic behavior, as the small parameter which characterizes the sizes of our two regions tends to zero, of the temperature field in the periodic composite. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)