The general question which will make the object of this paper is the homogenization of some nonlinear problems arising in the modelling of thermal diffusion in a two-component composite. We shall consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We shall deal with two situations: in the first one, we assume that we have some nonlinear sources acting in both components and that at the interface between our two materials the temperature and the flux are continuous, while in the second problem we shall address here, we assume that the flux is still continuous, but depends in a nonlinear way on the jump of the temperature field. In both cases, since the characteristic sizes of these two components are small compared with the macroscopic length-scale of the flow domain, we can apply an homogenization procedure.
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Timofte, C. (2008). Upscaling in Nonlinear Thermal Diffusion Problems in Composite Materials. In: Bonilla, L.L., Moscoso, M., Platero, G., Vega, J.M. (eds) Progress in Industrial Mathematics at ECMI 2006. Mathematics in Industry, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71992-2_46
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