Two-scale analysis for very rough thin layers. An explicit characterization of the polarization tensor
Language
en
Article de revue
This item was published in
Journal de Mathématiques Pures et Appliquées. 2011, vol. 95, n° 3, p. 227-295
Elsevier
English Abstract
We 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 ...Read more >
We 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 $\beta\geq1$.Read less <
Origin
Hal imported