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Corrector homogenization estimates for a non-stationary Stokes-Nernst-Planck-Poisson system in perforated domains
Gran Sasso Science Institute, Italy; Hasselt University, Belgium.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
2019 (English)In: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 17, no 3, p. 705-738Article in journal (Refereed) Published
Abstract [en]

We consider a non-stationary Stokes-Nernst-Planck-Poisson system posed in perforated domains. Our aim is to justify rigorously the homogenization limit for the upscaled system derived by means of two-scale convergence in [N. Ray, A. Muntean, and P. Knabner, J. Math. Anal. Appl., 390(1):374-393, 2012]. In other words, we wish to obtain the so-called corrector homogenization estimates that specify the error obtained when upscaling the microscopic equations. Essentially, we control in terms of suitable norms differences between the micro-and macro-concentrations and between the corresponding micro- and macro-concentration gradients. The major challenges that we face are the coupled flux structure of the system, the nonlinear drift terms and the presence of the microstructures. Employing various energy-like estimates, we discuss several scalings choices and boundary conditions.

Place, publisher, year, edition, pages
INT PRESS BOSTON , 2019. Vol. 17, no 3, p. 705-738
Keywords [en]
Stokes-Nernst-Planck-Poisson system, Variable scalings, Two-scale convergence, Perforated domains, Homogenization asymptotics, Corrector estimates
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-70797DOI: 10.4310/CMS.2019.v17.n3.a6ISI: 000485624800006OAI: oai:DiVA.org:kau-70797DiVA, id: diva2:1282488
Available from: 2019-01-24 Created: 2019-01-24 Last updated: 2019-12-19Bibliographically approved

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CiteExportLink to record
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  • apa
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