Scale limit of a variational inequality modeling diffusive flux in a domain with small holes and strong adsorption in case of a critical scaling |
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Authors: | W Jäger M Neuss-Radu T A Shaposhnikova |
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Institution: | 1.Interdisciplinary Center for Scientific Computing (IWR),University of Heidelberg Im Neuenheimer Feld 368,Heidelberg,Germany;2.Faculty of Mechanics and Mathematics,Moscow State University,Moscow,Russia |
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Abstract: | 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
0ɛα, 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−ασ(x, u
ɛ), u
ɛ(∂ν
u
ɛ + ɛ−ασ(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. |
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Keywords: | |
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