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Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit
Gran Sasso Sci Inst, Math & Comp Sci Div, Laquila, Italy..
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.ORCID iD: 0000-0002-1160-0007
2016 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 439, no 1, 271-295 p.Article in journal (Refereed) PublishedText
Abstract [en]

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. 

Place, publisher, year, edition, pages
2016. Vol. 439, no 1, 271-295 p.
Keyword [en]
Corrector estimates, Homogenization, Elliptic systems, Perforated domains
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-41993DOI: 10.1016/j.jmaa.2016.02.068ISI: 000372941500016OAI: oai:DiVA.org:kau-41993DiVA: diva2:927253
Available from: 2016-05-11 Created: 2016-05-11 Last updated: 2016-05-11Bibliographically approved

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Muntean, Adrian
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