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European Consortium for Mathematics in Industry

ECMI 2016: Progress in Industrial Mathematics at ECMI 2016 pp 617–623Cite as

Homogenization of a Hyperbolic-Parabolic Problem with Three Spatial Scales

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Part of the book series: Mathematics in Industry ((TECMI,volume 26))

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.

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References

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Author information

Authors and Affiliations

  1. Department of Quality Technology and Management, Mechanical Engineering and Mathematics, Mid Sweden University, S-83125, Östersund, Sweden

    Liselott Flodén, Anders Holmbom, Pernilla Jonasson, Marianne Olsson Lindberg, Tatiana Lobkova & Jens Persson

Authors
  1. Liselott Flodén
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  2. Anders Holmbom
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  3. Pernilla Jonasson
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  4. Marianne Olsson Lindberg
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  5. Tatiana Lobkova
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  6. Jens Persson
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Corresponding author

Correspondence to Marianne Olsson Lindberg .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Peregrina Quintela

  2. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Patricia Barral

  3. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Dolores Gómez

  4. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Francisco J. Pena

  5. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Jerónimo Rodríguez

  6. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Pilar Salgado

  7. Department of Applied Mathematics, University of Santiago de Compostela, Lugo, Spain, Spain

    Miguel E. Vázquez-Méndez

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Flodén, L., Holmbom, A., Jonasson, P., Lindberg, M.O., Lobkova, T., Persson, J. (2017). Homogenization of a Hyperbolic-Parabolic Problem with Three Spatial Scales. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_94

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