The limit behavior of the solutions of Signorini’s type-like problems in periodically perforated domains with period is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as . In the critical case, it is shown that Signorini’s problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming from the geometry; its appearance is due to the special size of the holes. The limit problem captures the two sources of oscillations involved in this kind of free boundary-value problems, namely, those arising from the size of the holes and those due to the periodic inhomogeneity of the medium. The main ingredient of the method used in the proof is an explicit construction of suitable test functions which provide a good understanding of the interactions between the above mentioned sources of oscillations.
Mots clés : Signorini's problem, homogenization, Tartar's method, variational inequality
@article{M2AN_2003__37_5_773_0, author = {Conca, Carlos and Murat, Fran\c{c}ois and Timofte, Claudia}, title = {A generalized strange term in {Signorini's} type problems}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {773--805}, publisher = {EDP-Sciences}, volume = {37}, number = {5}, year = {2003}, doi = {10.1051/m2an:2003055}, zbl = {1040.35008}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2003055/} }
TY - JOUR AU - Conca, Carlos AU - Murat, François AU - Timofte, Claudia TI - A generalized strange term in Signorini's type problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 773 EP - 805 VL - 37 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003055/ DO - 10.1051/m2an:2003055 LA - en ID - M2AN_2003__37_5_773_0 ER -
%0 Journal Article %A Conca, Carlos %A Murat, François %A Timofte, Claudia %T A generalized strange term in Signorini's type problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 773-805 %V 37 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003055/ %R 10.1051/m2an:2003055 %G en %F M2AN_2003__37_5_773_0
Conca, Carlos; Murat, François; Timofte, Claudia. A generalized strange term in Signorini's type problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 5, pp. 773-805. doi : 10.1051/m2an:2003055. http://www.numdam.org/articles/10.1051/m2an:2003055/
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