Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds |
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Authors: | D Gómez M Lobo TA Shaposhnikova |
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Institution: | 1. Departamento de Matemáticas, Estadística y Computación , Universidad de Cantabria , 39005 Santander , Spain;2. Department of Differential Equations , Moscow State University , 119992 Moscow , Russia |
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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 Ω? 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 ?α is the size of each cavity with α?≥?1; ? is a parameter that converges towards zero. Moreover, we also assume that the nonlinear process involves a large parameter ??κ with κ?=?(α???1)(n???1). Passing to the scale limit, and depending on the value of α, the effective equation or variational inequality is obtained. In particular, we find a critical size of the cavities when α?=?κ?=?(n???1)/(n???2). We also construct correctors which improve convergence for α?≥?(n???1)/(n???2). |
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Keywords: | porous media boundary homogenization variational inequalities nonlinear flux |
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