6533b851fe1ef96bd12a9885

RESEARCH PRODUCT

Modelling of Systems with a Dispersed Phase: “Measuring” Small Sets in the Presence of Elliptic Operators

Valeria Ricci

subject

Large number limitCapacityMathematical analysis010103 numerical & computational mathematics01 natural sciencesHomogenization (chemistry)010101 applied mathematicsTwo-component systemElliptic operatorBounded functionMathematics (all)Heat equation0101 mathematicsSettore MAT/07 - Fisica MatematicaMathematics

description

When modelling systems with a dispersed phase involving elliptic operators, as is the case of the Stokes or Navier-Stokes problem or the heat equation in a bounded domain, the geometrical structure of the space occupied by the dispersed phase enters in the homogenization process through its capacity, a quantity which can be used to define the equivalence classes in \(H^1\). We shall review the relationship between capacity and homogenization terms in the limit when the number of inclusions becomes large, focusing in particular on the situation where the distribution of inclusions is not necessarily too regular (i.e. it is not periodic).

yearjournalcountryeditionlanguage
2016-01-01
https://doi.org/10.1007/978-3-319-32144-8_14