Boundary homogenization in perforated domains for adsorption problems with an advection term. Issue 7 (2nd July 2016) - Brillard, A.; Gómez, D.; Lobo, M.; Pérez, E.; Shaposhnikova, T. A.
Abstract : We consider a model for the spreading of a substance through an incompressible fluid in a perforated domain, with . The fluid flows in a domain containing a periodical set of perforations ( ) placed along an inner surface . The size of the perforations is much smaller than the size of the characteristic period . An adsorption phenomena can occur on the boundaries of the perforations, where we assume a strongly nonlinear adsorption law with a large adsorption parameter. An advection term appears in the partial differential equation. We obtain the homogenized model which also involves a nonlinear transmission condition for the normal derivative on . The 'strange term' arising in this transmission condition is a nonlinear function implicitly defined by a functional equation. We deal with critical relations both for the size of perforations and the adsorption parameter while we use the energy method for variational inequalities to show the convergence.