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Multi-scale analysis for highly anisotropic parabolic problems

Thomas Blanc
Mihai Bostan
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Abstract

We focus on the asymptotic behavior of strongly anisotropic parabolic problems. We concentrate on heat equations, whose diffusion matrix fields have disparate eigen-values. 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.
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Dates and versions

hal-01654430 , version 1 (04-12-2017)
hal-01654430 , version 2 (01-02-2018)

Identifiers

  • HAL Id : hal-01654430 , version 2

Cite

Thomas Blanc, Mihai Bostan. Multi-scale analysis for highly anisotropic parabolic problems. 2018. ⟨hal-01654430v2⟩
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