Homogenization of some parabolic operators with several time scales

Liselott Flodén; Marianne Olsson

Applications of Mathematics (2007)

  • Volume: 52, Issue: 5, page 431-446
  • ISSN: 0862-7940

Abstract

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The main focus in this paper is on homogenization of the parabolic problem ∂ t u ε - ∇ · ( a ( x / ε , t / ε , t / ε r ) ∇ u ε ) = f . Under certain assumptions on a , there exists a G -limit b , which we characterize by means of multiscale techniques for r > 0 , r ≠ 1 . Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made.

How to cite

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Flodén, Liselott, and Olsson, Marianne. "Homogenization of some parabolic operators with several time scales." Applications of Mathematics 52.5 (2007): 431-446. <http://eudml.org/doc/33300>.

@article{Flodén2007,
abstract = {The main focus in this paper is on homogenization of the parabolic problem $ \partial _\{t\}u^\{\varepsilon \}-\nabla \cdot ( a( \{x\}/\{\varepsilon \},\{t\}/\{\varepsilon \}, \{t\}/\{\varepsilon ^\{r\}\})\nabla u^\{\varepsilon \}) =f$. Under certain assumptions on $a$, there exists a $G$-limit $b$, which we characterize by means of multiscale techniques for $r>0$, $r\ne 1$. Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made.},
author = {Flodén, Liselott, Olsson, Marianne},
journal = {Applications of Mathematics},
keywords = {homogenization; $G$-convergence; multiscale convergence; parabolic; asymptotic expansion; homogenization; -convergence; multiscale convergence; parabolic equation; asymptotic expansion},
language = {eng},
number = {5},
pages = {431-446},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homogenization of some parabolic operators with several time scales},
url = {http://eudml.org/doc/33300},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Flodén, Liselott
AU - Olsson, Marianne
TI - Homogenization of some parabolic operators with several time scales
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 5
SP - 431
EP - 446
AB - The main focus in this paper is on homogenization of the parabolic problem $ \partial _{t}u^{\varepsilon }-\nabla \cdot ( a( {x}/{\varepsilon },{t}/{\varepsilon }, {t}/{\varepsilon ^{r}})\nabla u^{\varepsilon }) =f$. Under certain assumptions on $a$, there exists a $G$-limit $b$, which we characterize by means of multiscale techniques for $r>0$, $r\ne 1$. Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made.
LA - eng
KW - homogenization; $G$-convergence; multiscale convergence; parabolic; asymptotic expansion; homogenization; -convergence; multiscale convergence; parabolic equation; asymptotic expansion
UR - http://eudml.org/doc/33300
ER -

References

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