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Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1752-1211
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-2185-641x
2018 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 89-106Article in journal (Refereed) Published
Abstract [en]

We establish the well-posedness of a coupled micro–macro parabolic– elliptic system modeling the interplay between two pressures in a gas–liquid mixture close to equilibrium that is filling a porous media with distributed microstructures. Additionally, we prove a local stability estimate for the inverse micro–macro Robin problem, potentially useful in identifying quantitatively a micro–macro interfacial Robin transfer coefficient given microscopic measurements on accessible fixed interfaces. To tackle the solvability issue we use two-scale energy estimates and twoscale regularity/compactness arguments cast in the Schauder’s fixed point theorem. A number of auxiliary problems, regularity, and scaling arguments are used in ensuring the suitable Fréchet differentiability of the solution and the structure of the inverse stability estimate.

Place, publisher, year, edition, pages
Taylor & Francis, 2018. Vol. 97, no 1, p. 89-106
Keywords [en]
Upscaled porous media, two-scale PDE, inverse micro–macro Robin problem
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-62809DOI: 10.1080/00036811.2017.1364366OAI: oai:DiVA.org:kau-62809DiVA, id: diva2:1136119
Available from: 2017-08-25 Created: 2017-08-25 Last updated: 2018-06-12Bibliographically approved

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Lind, MartinMuntean, AdrianRichardson, Omar

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CiteExportLink to record
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  • apa
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  • fi-FI
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  • Other locale
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Output format
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