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Multi-scale analysis for highly anisotropic parabolic problems

  • * Corresponding author: Mihaï Bostan

    * Corresponding author: Mihaï Bostan
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  • We focus on the asymptotic behavior of strongly anisotropic parabolic problems. We concentrate on heat equations, whose diffusion matrix fields have disparate eigenvalues. We establish strong convergence results toward a profile. Under suitable smoothness hypotheses, by introducing an appropriate corrector term, we estimate the convergence rate. The arguments rely on two-scale analysis, based on average operators with respect to unitary groups.

    Mathematics Subject Classification: Primary: 35K05; Secondary: 37A10.


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