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Published in:
2017 | OriginalPaper | Chapter
Homogenization of a Hyperbolic-Parabolic Problem with Three Spatial Scales
Authors : Liselott Flodén, Anders Holmbom, Pernilla Jonasson, Marianne Olsson Lindberg, Tatiana Lobkova, Jens Persson
Published in: Progress in Industrial Mathematics at ECMI 2016
Publisher: Springer International Publishing
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Abstract
We study the homogenization of a certain linear hyperbolic-parabolic problem exhibiting two rapid spatial scales {ε, ε
2}. The homogenization is performed by means of evolution multiscale convergence, a generalization of the concept of two-scale convergence to include any number of scales in both space and time. In particular we apply a compactness result for gradients. The outcome of the homogenization procedure is that we obtain a homogenized problem of hyperbolic-parabolic type together with two elliptic local problems, one for each rapid scale.