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Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales

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Abstract

We prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of the scale parameter ε. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evolution problems.

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Acknowledgment

We would like to thank the anonymous referee for valuable comments that have improved the quality of the paper.

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Authors and Affiliations

  1. Department of Engineering, Mathematics and Science Education, Mid Sweden University, Kunskapens väg 8, S-83125, Östersund, Sweden

    Tatiana Danielsson, Liselott Flodén, Pernilla Johnsen & Marianne Olsson Lindberg

Authors
  1. Tatiana Danielsson
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  2. Liselott Flodén
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  3. Pernilla Johnsen
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  4. Marianne Olsson Lindberg
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Corresponding author

Correspondence to Liselott Flodén.

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In memory of Anders Holmbom (1958–2022)

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Danielsson, T., Flodén, L., Johnsen, P. et al. Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales. Appl Math 69, 1–24 (2024). https://doi.org/10.21136/AM.2023.0269-22

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