# A Generalized Strange Term in Signorini's Type Problems

Carlos Conca; François Murat; Claudia Timofte

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 37, Issue: 5, page 773-805
- ISSN: 0764-583X

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topConca, Carlos, Murat, François, and Timofte, Claudia. "A Generalized Strange Term in Signorini's Type Problems." ESAIM: Mathematical Modelling and Numerical Analysis 37.5 (2010): 773-805. <http://eudml.org/doc/194191>.

@article{Conca2010,

abstract = {
The limit behavior of the solutions of Signorini's type-like
problems in periodically perforated domains with period
ε 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 ε → 0. 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.
},

author = {Conca, Carlos, Murat, François, Timofte, Claudia},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Signorini's problem;
homogenization; Tartar's method; variational inequality.; periodically perforated domains; extra zero-order term},

language = {eng},

month = {3},

number = {5},

pages = {773-805},

publisher = {EDP Sciences},

title = {A Generalized Strange Term in Signorini's Type Problems},

url = {http://eudml.org/doc/194191},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Conca, Carlos

AU - Murat, François

AU - Timofte, Claudia

TI - A Generalized Strange Term in Signorini's Type Problems

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 5

SP - 773

EP - 805

AB -
The limit behavior of the solutions of Signorini's type-like
problems in periodically perforated domains with period
ε 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 ε → 0. 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.

LA - eng

KW - Signorini's problem;
homogenization; Tartar's method; variational inequality.; periodically perforated domains; extra zero-order term

UR - http://eudml.org/doc/194191

ER -

## References

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