Homogenization of a Hyperbolic-Parabolic Problem with Three Spatial Scales

  • Liselott Flodén
  • Anders Holmbom
  • Pernilla Jonasson
  • Marianne Olsson Lindberg
  • Tatiana Lobkova
  • Jens Persson
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

We study the homogenization of a certain linear hyperbolic-parabolic problem exhibiting two rapid spatial scales {ε, ε2}. 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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Liselott Flodén
    • 1
  • Anders Holmbom
    • 1
  • Pernilla Jonasson
    • 1
  • Marianne Olsson Lindberg
    • 1
  • Tatiana Lobkova
    • 1
  • Jens Persson
    • 1
  1. 1.Department of Quality Technology and Management, Mechanical Engineering and MathematicsMid Sweden UniversityÖstersundSweden

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