Scale limit of a variational inequality modeling diffusive flux in a domain with small holes and strong adsorption in case of a critical scaling
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
15 May 2011
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| In: |
Doklady mathematics
Year: 2011, Volume: 83, Issue: 2, Pages: 204-208 |
| ISSN: | 1531-8362 |
| DOI: | 10.1134/S1064562411020219 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1134/S1064562411020219 Verlag, Volltext: https://link.springer.com/article/10.1134/S1064562411020219 
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| Author Notes: | W. Jäger, M. Neuss-Radu, and T.A. Shaposhnikova |
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| 520 | |a 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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