Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions

• Rigorous homogenization of parabolic problems in evolving micro-domains. Reaction-diffusion-advection equations with nonlinear boundary conditions. Strong two-scale compactness result Kolmogorov-Simon-type. We consider a reaction-diffusion-advection problem perforated medium, reactions the bulk and at microscopic boundary, slow diffusion scaling. The microstructure changes time; microstructural evolution is known priori . aim paper rigorous derivation homogenized model. use appropriately scaled function spaces, which allow us to show results, especially regarding time-derivative we prove strong results Kolmogorov-Simon-type, pass limit terms. derived macroscopic model depends on micro- macro-variable, underlying approximated by time- space-dependent reference elements.