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On a pore-scale stationary diffusion equation: Scaling effects and correctors for the homogenization limit
Hasselt University, BEL; Univ North Carolina Charlotte, USA.ORCID iD: 0000-0003-4233-0895
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Gran Sasso Sci Inst, ITA.ORCID iD: 0000-0002-5887-5040
Meiji Inst Adv Study Math Sci, JPN.
2021 (English)In: Discrete and continuous dynamical systems. Series B, ISSN 1531-3492, E-ISSN 1553-524X, Vol. 26, no 5, p. 2451-2477Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider a microscopic semilinear elliptic equation posed in periodically perforated domains and associated with the Fourier-type condition on internal micro-surfaces. The first contribution of this work is the construction of a reliable linearization scheme that allows us, by a suitable choice of scaling arguments and stabilization constants, to prove the weak solvability of the microscopic model. Asymptotic behaviors of the microscopic solution with respect to the microscale parameter are thoroughly investigated in the second theme, based upon several cases of scaling. In particular, the variable scaling illuminates the trivial and non-trivial limits at the macroscale, confirmed by certain rates of convergence. Relying on classical results for homogenization of multiscale elliptic problems, we design a modified two-scale asymptotic expansion to derive the corresponding macroscopic equation, when the scaling choices are compatible. Moreover, we prove the high-order corrector estimates for the homogenization limit in the energy space H-1, using a large amount of energy-like estimates. A numerical example is provided to corroborate the asymptotic analysis.

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2021. Vol. 26, no 5, p. 2451-2477
Keywords [en]
Pore-scale model, nonlinear elliptic equations, perforated domains, linearization, asymptotic analysis, corrector estimates
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-83604DOI: 10.3934/dcdsb.2020190ISI: 000624972400007Scopus ID: 2-s2.0-85108500440OAI: oai:DiVA.org:kau-83604DiVA, id: diva2:1543172
Available from: 2021-04-09 Created: 2021-04-09 Last updated: 2021-07-02Bibliographically approved

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Thoa Thieu, T.K.

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