On the Steklov problem in a domain perforated along a part of the boundary

Author: Chechkin Gregory A.   Gadyl’shin Rustem R.   D’Apice Ciro   De Maio Umberto  

Publisher: Edp Sciences

E-ISSN: 1290-3841|51|4|1317-1342

ISSN: 0764-583x

Source: ESAIM: Mathematical Modelling and Numerical Analysis, Vol.51, Iss.4, 2017-07, pp. : 1317-1342

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Abstract

We study the asymptotic behavior of solutions and eigenelements to a 2-dimensional and 3-dimensional boundary value problem for the Laplace equation in a domain perforated along part of the boundary. On the boundary of holes we set the homogeneous Dirichlet boundary condition and the Steklov spectral condition on the mentioned part of the outer boundary of the domain. Assuming that the boundary microstructure is periodic, we construct the limit problem and prove the homogenization theorem.