Publication Date:
2011-06-10
Description:
In this paper we study the asymptotic behavior of solutions u ɛ of the elliptic variational inequality for the Laplace operator in domains periodically perforated by balls with radius of size C 0 ɛ α , C 0 〉 0, α = n / n −2, and distributed with period ɛ. On the boundary of balls, we have the following nonlinear restrictions u ɛ ≥ 0, ∂ ν u ɛ ≥ −ɛ −α σ( x, u ɛ ), u ɛ (∂ ν u ɛ + ɛ −α σ( x, u ɛ )) = 0. The weak convergence of the solutions u ɛ to the solution of an effective variational equality is proved. In this case, the effective equation contains a nonlinear term which has to be determined as solution of a functional equation. Furthermore, a corrector result with respect to the energy norm is given. Content Type Journal Article Pages 204-208 DOI 10.1134/S1064562411020219 Authors W. Jäger, Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg Im Neuenheimer Feld 368, 69120 Heidelberg, Germany M. Neuss-Radu, Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg Im Neuenheimer Feld 368, 69120 Heidelberg, Germany T. A. Shaposhnikova, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992 Russia Journal Doklady Mathematics Online ISSN 1531-8362 Print ISSN 1064-5624 Journal Volume Volume 83 Journal Issue Volume 83, Number 2
Print ISSN:
1064-5624
Electronic ISSN:
1531-8362
Topics:
Mathematics
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