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Two-scale analysis for very rough thin layers. An explicit characterization of the polarization tensor

hal.structure.identifierInstitut Camille Jordan [ICJ]
dc.contributor.authorCIUPERCA, Ionel Sorin
hal.structure.identifierAmpère [AMPERE]
dc.contributor.authorPERRUSSEL, Ronan
hal.structure.identifierModélisation, contrôle et calcul [MC2]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPOIGNARD, Clair
dc.date.created2009
dc.date.issued2011
dc.identifier.issn0021-7824
dc.description.abstractEnWe study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a very rough thin layer and embedded in an ambient medium. The roughness of the layer is described by a quasi $\eps$--periodic function, $\eps$ being a small parameter, while the mean thickness of the layer is of magnitude $\eps^\beta$, where $\beta\in(0,1)$. Using the two-scale analysis, we replace the very rough thin layer by appropriate transmission conditions on the boundary of the object, which lead to an explicit characterization of the polarization tensor of Vogelius and Capdeboscq (ESAIM:M2AN. 2003; 37:159-173). This paper extends the previous works Poignard (Math. Meth. App. Sci. 2009; 32:435-453) and Ciuperca \textsl{et al.} (Research report INRIA RR-6812), in which $\beta\geq1$.
dc.language.isoen
dc.publisherElsevier
dc.title.enTwo-scale analysis for very rough thin layers. An explicit characterization of the polarization tensor
dc.typeArticle de revue
dc.identifier.doi10.1016/j.matpur.2010.12.001
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalJournal de Mathématiques Pures et Appliquées
bordeaux.page227-295
bordeaux.volume95
bordeaux.issue3
bordeaux.peerReviewedoui
hal.identifierinria-00401835
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//inria-00401835v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20Math%C3%A9matiques%20Pures%20et%20Appliqu%C3%A9es&rft.date=2011&rft.volume=95&rft.issue=3&rft.spage=227-295&rft.epage=227-295&rft.eissn=0021-7824&rft.issn=0021-7824&rft.au=CIUPERCA,%20Ionel%20Sorin&PERRUSSEL,%20Ronan&POIGNARD,%20Clair&rft.genre=article


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