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Homogenization of a locally periodic time-dependent domain

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  • We consider the homogenization of a Robin boundary value problem in a locally periodic perforated domain which is also time-dependent. We aim at justifying the homogenization limit, that we derive through asymptotic expansion technique. More exactly, we obtain the so-called corrector homogenization estimate that specifies the convergence rate. The major challenge is that the media is not cylindrical and changes over time. We also show the existence and uniqueness of solutions of the microscopic problem.

    Mathematics Subject Classification: Primary: 35B27, 35K57; Secondary: 74Q10.

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  • Figure 1.  Schematic representation of a locally periodic heterogeneous medium in a time slice

    Figure 2.  Schematic a non-cylindrical domain approximated by a family of cylindrical domains

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