Open this publication in new window or tab >>2013 (English)In: Pure and Applied Mathematics Quarterly, ISSN 1558-8599, E-ISSN 1558-8602, Vol. 9, no 3, p. 461-486Article in journal (Refereed) Published
Abstract [en]
We first study the fundamental ideas behind two-scale conver-
gence to enhance an intuitive understanding of this notion. The classical
definitions and ideas are motivated with geometrical arguments illustrated
by illuminating figures. Then a version of this concept, very weak two-scale
convergence, is discussed both independently and brie°y in the context of
homogenization. The main features of this variant are that it works also
for certain sequences of functions which are not bounded in
L2 and at
the same time is suited to detect rapid oscillations in some sequences which
are strongly convergent in
L2 . In particular, we show how very weak
two-scale convergence explains in a more transparent way how the oscilla-
tions of the governing coe±cient of the PDE to be homogenized causes the
deviation of the
G-limit from the weak L2 NxN-limit for the sequence of
coe±cients. Finally, we investigate very weak multiscale convergence and
prove a compactness result for separated scales which extends a previous
result which required well-separated scales.
Place, publisher, year, edition, pages
International press of Boston, 2013
Keywords
Two-scale convergence, multiscale convergence, very weak multiscale convergence, homogenization
National Category
Natural Sciences Mathematics
Identifiers
urn:nbn:se:miun:diva-20401 (URN)10.4310/PAMQ.2013.v9.n3.a4 (DOI)000327544500004 ()2-s2.0-84887587258 (Scopus ID)
2013-12-022013-12-022017-12-06Bibliographically approved