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.
Accepté le :
DOI : 10.1051/m2an/2016063
Mots clés : Homogenization, the Steklov spectral problem, asymptotic methods
@article{M2AN_2017__51_4_1317_0, author = {Chechkin, Gregory A. and Gadyl{\textquoteright}shin, Rustem R. and D{\textquoteright}Apice, Ciro and De Maio, Umberto}, title = {On the {Steklov} problem in a domain perforated along a part of the boundary}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1317--1342}, publisher = {EDP-Sciences}, volume = {51}, number = {4}, year = {2017}, doi = {10.1051/m2an/2016063}, mrnumber = {3702415}, zbl = {1378.35020}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016063/} }
TY - JOUR AU - Chechkin, Gregory A. AU - Gadyl’shin, Rustem R. AU - D’Apice, Ciro AU - De Maio, Umberto TI - On the Steklov problem in a domain perforated along a part of the boundary JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1317 EP - 1342 VL - 51 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016063/ DO - 10.1051/m2an/2016063 LA - en ID - M2AN_2017__51_4_1317_0 ER -
%0 Journal Article %A Chechkin, Gregory A. %A Gadyl’shin, Rustem R. %A D’Apice, Ciro %A De Maio, Umberto %T On the Steklov problem in a domain perforated along a part of the boundary %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1317-1342 %V 51 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016063/ %R 10.1051/m2an/2016063 %G en %F M2AN_2017__51_4_1317_0
Chechkin, Gregory A.; Gadyl’shin, Rustem R.; D’Apice, Ciro; De Maio, Umberto. On the Steklov problem in a domain perforated along a part of the boundary. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1317-1342. doi : 10.1051/m2an/2016063. http://www.numdam.org/articles/10.1051/m2an/2016063/
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