Some remarks on two-scale convergence and periodic unfolding

Jan Franců; Nils E M Svanstedt

Applications of Mathematics (2012)

  • Volume: 57, Issue: 4, page 359-375
  • ISSN: 0862-7940

Abstract

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The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization to non-periodic homogenization.

How to cite

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Franců, Jan, and Svanstedt, Nils E M. "Some remarks on two-scale convergence and periodic unfolding." Applications of Mathematics 57.4 (2012): 359-375. <http://eudml.org/doc/246815>.

@article{Franců2012,
abstract = {The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization to non-periodic homogenization.},
author = {Franců, Jan, Svanstedt, Nils E M},
journal = {Applications of Mathematics},
keywords = {two-scale convergence; unfolding; homogenization; two-scale convergence; unfolding; homogenization},
language = {eng},
number = {4},
pages = {359-375},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some remarks on two-scale convergence and periodic unfolding},
url = {http://eudml.org/doc/246815},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Franců, Jan
AU - Svanstedt, Nils E M
TI - Some remarks on two-scale convergence and periodic unfolding
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 359
EP - 375
AB - The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization to non-periodic homogenization.
LA - eng
KW - two-scale convergence; unfolding; homogenization; two-scale convergence; unfolding; homogenization
UR - http://eudml.org/doc/246815
ER -

References

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