Journal article

A note on parabolic homogenization with a mismatch between the spatial scales

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Publication Details

Author list: HOLMBOM A, OLSSON LINDBERG M, FLODEN L, HOLMBOM A, OLSSON LINDBERG M, Persson J, FLODEN L

Publisher: Hindawi Publishing Corporation

Publication year: 2013

Start page: Art. no. 329704

ISSN: 1085-3375

DOI: http://dx.doi.org/10.1155/2013/329704

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Abstract

We consider the homogenization of the linear parabolic problem rho(x/epsilon(2))partial derivative(t)u(epsilon)(x,t) - del . (a(x/epsilon(1), t/epsilon(2)(1))del u(epsilon) (x,t)) = f(x,t) which exhibits a mismatch between the spatial scales in the sense that the coefficient a(x/epsilon(1), t/epsilon(2)(1)) of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient rho(x/epsilon(2)) of the time derivative contains a faster spatial scale. It is shown that the faster spatialmicroscale does not give rise to any corrector termand that there is only one local problemneeded 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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