Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit

作者：Khoa Vo Anh^*; Muntean Adrian

来源：Journal of Mathematical Analysis and Applications, 2016, 439(1): 271-295.

DOI：10.1016/j.jmaa.2016.02.068

• Corrector estimates
• Homogenization
• Elliptic systems
• Perforated domains

In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then use the structure of the two scale expansions to derive corrector estimates delimitating this way the convergence rate of the asymptotic approximates to the macroscopic limit concentrations. Our techniques include Moser-like iteration techniques, a variational formulation, two scale asymptotic expansions as well as energy-like estimates.

• 出版日期2016-7-1