Homogenization of monotone parabolic problems with several temporal scales

Jens Persson

Applications of Mathematics (2012)

  • Volume: 57, Issue: 3, page 191-214
  • ISSN: 0862-7940

Abstract

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In this paper we homogenize monotone parabolic problems with two spatial scales and any number of temporal scales. Under the assumption that the spatial and temporal scales are well-separated in the sense explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the “slow” self-similar case), rapid temporal oscillations, and rapid resonant spatial and temporal oscillations (the ``rapid'' self-similar case), respectively.

How to cite

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Persson, Jens. "Homogenization of monotone parabolic problems with several temporal scales." Applications of Mathematics 57.3 (2012): 191-214. <http://eudml.org/doc/246651>.

@article{Persson2012,
abstract = {In this paper we homogenize monotone parabolic problems with two spatial scales and any number of temporal scales. Under the assumption that the spatial and temporal scales are well-separated in the sense explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the “slow” self-similar case), rapid temporal oscillations, and rapid resonant spatial and temporal oscillations (the ``rapid'' self-similar case), respectively.},
author = {Persson, Jens},
journal = {Applications of Mathematics},
keywords = {homogenization; $H$-convergence; multiscale convergence; parabolic; monotone; parabolic problem; homogenization; -convergence; multiscale convergence; parabolic problem},
language = {eng},
number = {3},
pages = {191-214},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homogenization of monotone parabolic problems with several temporal scales},
url = {http://eudml.org/doc/246651},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Persson, Jens
TI - Homogenization of monotone parabolic problems with several temporal scales
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 191
EP - 214
AB - In this paper we homogenize monotone parabolic problems with two spatial scales and any number of temporal scales. Under the assumption that the spatial and temporal scales are well-separated in the sense explained in the paper, we show that there is an H-limit defined by at most four distinct sets of local problems corresponding to slow temporal oscillations, slow resonant spatial and temporal oscillations (the “slow” self-similar case), rapid temporal oscillations, and rapid resonant spatial and temporal oscillations (the ``rapid'' self-similar case), respectively.
LA - eng
KW - homogenization; $H$-convergence; multiscale convergence; parabolic; monotone; parabolic problem; homogenization; -convergence; multiscale convergence; parabolic problem
UR - http://eudml.org/doc/246651
ER -

References

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Citations in EuDML Documents

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  1. Pernilla Johnsen, Tatiana Lobkova, Homogenization of a linear parabolic problem with a certain type of matching between the microscopic scales
  2. Tatiana Danielsson, Pernilla Johnsen, Homogenization of linear parabolic equations with three spatial and three temporal scales for certain matchings between the microscopic scales
  3. Abdelhakim Dehamnia, Hamid Haddadou, Multiscale homogenization of nonlinear hyperbolic-parabolic equations
  4. Tatiana Danielsson, Liselott Flodén, Pernilla Johnsen, Marianne Olsson Lindberg, Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales

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