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Bloch Approximation in Homogenization and Applications

dc.contributor.authorConca Rosende, Carlos
dc.contributor.authorOrive, R.
dc.contributor.authorVanninathan, Muthusamy
dc.date.accessioned2023-06-20T16:48:28Z
dc.date.available2023-06-20T16:48:28Z
dc.date.issued2002-04-11
dc.description.abstractThe classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions $u^\varepsilon$ of boundary value problems associated with such operators when the period $\varepsilon>0$ of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as $\varepsilon\to 0$ towards the homogenized solution was furnished using Bloch wave decomposition. Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution $u^\varepsilon$. We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to capture the oscillations of the solution in a sharper way. The present approach sheds new light and offers an alternative for viewing classical results.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipDGES
dc.description.sponsorshipEU TRM Network
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/12905
dc.identifier.doi10.1137/S0036141001382200
dc.identifier.issn0036-1410
dc.identifier.officialurlhttp://epubs.siam.org/sima/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57083
dc.issue.number5
dc.journal.titleSiam Journal on Mathematical Analysis
dc.language.isoeng
dc.page.final1198
dc.page.initial1166
dc.publisherSociety for Industrial and Applied Mathematics
dc.relation.projectIDPB 96-0663
dc.relation.projectIDTRM
dc.rights.accessRightsopen access
dc.subject.cdu517.986.6
dc.subject.cdu517.518
dc.subject.keywordHomogenization
dc.subject.keywordBloch waves
dc.subject.keywordCorrectors
dc.subject.ucmAnálisis matemático
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleBloch Approximation in Homogenization and Applications
dc.typejournal article
dc.volume.number33
dspace.entity.typePublication

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