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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 329704, 6 pages
http://dx.doi.org/10.1155/2013/329704
Research Article

A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales

Department of Quality Technology and Management, Mechanical Engineering and Mathematics, Mid Sweden University, 83125 Östersund, Sweden

Received 16 May 2013; Accepted 29 August 2013

Academic Editor: Rodrigo Lopez Pouso

Copyright © 2013 Liselott Flodén et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the homogenization of the linear parabolic problem which exhibits a mismatch between the spatial scales in the sense that the coefficient of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient 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.