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Hypertemperature effects in heterogeneous media and thermal flux at small-length scales
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-4403-6908
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
2023 (English)In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 18, no 3, p. 1207-1225Article in journal (Refereed) Published
Abstract [en]

We propose an enriched microscopic heat conduction model that can account for size effects in heterogeneous media. Benefiting from physically relevant scaling arguments, we improve the regularity of the corrector in the classical problem of periodic homogenization of linear elliptic equations in the three-dimensional setting and, while doing so, we clarify the intimate role that correctors play in measuring the difference between the heterogeneous solution (microscopic) and the homogenized solution (macroscopic). Moreover, if the data are of form f = div F with (Formula presented), then we recover the classical corrector convergence theorem. 

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2023. Vol. 18, no 3, p. 1207-1225
Keywords [en]
correctors, scale-size thermal effects, generalized Fourier's law, microstructure
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-93953DOI: 10.3934/nhm.2023052ISI: 001039377000012Scopus ID: 2-s2.0-85158820491OAI: oai:DiVA.org:kau-93953DiVA, id: diva2:1744076
Funder
Knowledge Foundation, 2020-0152Available from: 2023-03-16 Created: 2023-03-16 Last updated: 2023-08-24Bibliographically approved

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Nika, GrigorMuntean, Adrian

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