Publication detail

Some remarks on two-scale convergence and periodic unfolding

FRANCŮ, J. SVANSTEDT, N.

Czech title

Několik poznámek o dvojškálové konvergenci a periodickém rozvinutí

English title

Some remarks on two-scale convergence and periodic unfolding

Type

journal article - other

Language

en

Original 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.

Czech abstract

Článek se zabývá některými aspekty duální definice dvojškálové konvergence založené na periodickém rozvinutí. Tento přínos odstraňuje problémy s volbou vhodného prostoru pro přípustné testovací funkce. Článek navrhuje modifikované rozvinutí, které zachovává hodnotu integrálu rozvinuté funkce a tudíž zjednodušuje důkazy a aplikace v teorii homogenizace. Článek poskytuje také úvod do dvojškálové konvergence a dává idee pro zobecnění na neperiodickou homogenizaci.

English 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.

Keywords in Czech

dvojškálová konvergence, rozvinutí, homogenizace

Keywords in English

two-scale convergence, unfolding, homogenization

RIV year

2012

Released

15.07.2012

Publisher

Matematický ústav AVČR

Location

Praha

ISSN

0373-6725

Volume

57

Number

4

Pages from–to

359–375

Pages count

16

BIBTEX


@article{BUT88496,
  author="Jan {Franců} and Nils E M {Svanstedt},
  title="Some remarks on two-scale convergence and periodic unfolding",
  year="2012",
  volume="57",
  number="4",
  month="July",
  pages="359--375",
  publisher="Matematický ústav AVČR",
  address="Praha",
  issn="0373-6725"
}