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The aim of this paper is to study the asymptotic behavior of the solution of a convection-diffusion equation in perforated domains with oscillating velocity and a Robin boundary condition which describes the adsorption on the bord of the obstacles. Without any periodicity assumption, for a large range of perforated media and by mean of variational homogenization, we find the global behavior when the characteristic size ε of the perforations tends to zero. The homogenized model, is a convection-diffusion equation but with an extra term coming from the weak adsorption boundary condition. An example is presented to illustrate the methodology.

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SUMMARYWe study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain (") of asymptotically degenerating measure, i.e. meas (") → 0 as " → 0, where " is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium (") associated with our problem in a variational form.