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Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds

Abstract: In this article, we consider variational inequalities arising, e.g., in modelling diffusion of substances in porous media. We assume that the media fills a domain ?? of ? n with n???3. We study the case where the number of cavities is large and they are periodically distributed along a (n???1)-dimensional manifold. ? is the period while ?? is the size of each cavity with ????1; ? is a parameter that converges towards zero. Moreover, we also assume that the nonlinear process involves a large parameter ??? with ??=?(????1)(n???1). Passing to the scale limit, and depending on the value of ?, the effective equation or variational inequality is obtained. In particular, we find a critical size of the cavities when ??=???=?(n???1)/(n???2). We also construct correctors which improve convergence for ????(n???1)/(n???2).

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Autoría: Gómez D., Lobo M., Pérez M., Shaposhnikova T.,

 Fuente: Applicable Analysis, 2013, 92(2), 218-237

Editorial: Gordon and Breach

 Año de publicación: 2013

Tipo de publicación: Artículo de Revista

 DOI: 10.1080/00036811.2011.602635

ISSN: 0003-6811,1563-504X,1026-7360

Url de la publicación: https://www.tandfonline.com/doi/abs/10.1080/00036811.2011.602635