In the book by U. Hornung, Chapter 6, the author proposes an homogenization strategy for the effective behavior of some chemical processes involving adsorption and reactions arising in porous media. Rigorous proofs of the convergence results are given in the case of linear adsorption rates and linear chemical reactions. The author leaves as an open question the case of a nonlinear adsorption rate. Our goal in this paper is to study two well-known examples of such nonlinear models, namely the so-called Freundlich and Langmuir kinetics.

We study the overall thermal conductivity of a composite material obtained by inserting in a hosting medium an array of finely mixed inclusions made of perfect heat conductors. The physical properties of this material are useful in applications and are obtained using the periodic unfolding method. The peculiarity of this problem calls for a suitable choice of test functions in the unfolding procedure, which leads to a non-standard variational two-scale problem, that cannot be written in a strong form, as usual.

We study the thermal properties of a composite material in which a periodic array of finely mixed perfect thermal conductors is inserted. The suitable model describing the behaviour of such physical materials leads to the so-called equivalued surface boundary value problem. To analyze the overall conductivity of the composite medium (when the size of the inclusions tends to zero), we make use of the homogenization theory, employing the unfolding technique. The peculiarity of the problem under investigation asks for a particular care in developing the unfolding procedure, giving rise to a non-standard two-scale problem.

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