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2013 A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales
Liselott Flodén, Anders Holmbom, Marianne Olsson Lindberg, Jens Persson
Abstr. Appl. Anal. 2013(SI29): 1-6 (2013). DOI: 10.1155/2013/329704

Abstract

We consider the homogenization of the linear parabolic problem ρ ( x / ε 2 ) t u ε ( x , t ) - · ( a ( x / ε 1 , t / ε 1 2 ) u ε ( x , t ) ) = f ( x , t ) which exhibits a mismatch between the spatial scales in the sense that the coefficient a ( x / ε 1 , t / ε 1 2 ) of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient ρ ( x / ε 2 ) of the time derivative contains a faster spatial scale. It is shown that the faster spatial microscale does not give rise to any corrector term and that there is only one local problem needed to characterize the homogenized problem. Hence, the problem is not of a reiterated type even though two rapid scales of spatial oscillation appear.

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Liselott Flodén. Anders Holmbom. Marianne Olsson Lindberg. Jens Persson. "A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales." Abstr. Appl. Anal. 2013 (SI29) 1 - 6, 2013. https://doi.org/10.1155/2013/329704

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1293.35027
MathSciNet: MR3111807
Digital Object Identifier: 10.1155/2013/329704

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI29 • 2013
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