## Abstract and Applied Analysis

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

#### Abstract

We consider the homogenization of the linear parabolic problem $\rho (x{/\epsilon }_{\mathrm{2}}){\partial }_{t}{u}^{\epsilon }(x,t)-\nabla ·(a(x/{\epsilon }_{\mathrm{1}},t/{\epsilon }_{\mathrm{1}}^{\mathrm{2}})\nabla {u}^{\epsilon }(x,t))=f(x,t)$ which exhibits a mismatch between the spatial scales in the sense that the coefficient $a(x{/\epsilon }_{\mathrm{1}},t/{\epsilon }_{\mathrm{1}}^{\mathrm{2}})$ of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient $\rho (x/{\epsilon }_{\mathrm{2}})$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 329704, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393449746

Digital Object Identifier
doi:10.1155/2013/329704

Mathematical Reviews number (MathSciNet)
MR3111807

Zentralblatt MATH identifier
1293.35027

#### Citation

Flodén, Liselott; Holmbom, Anders; Olsson Lindberg, Marianne; Persson, Jens. A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 329704, 6 pages. doi:10.1155/2013/329704. https://projecteuclid.org/euclid.aaa/1393449746

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