Multi-scale analysis for highly anisotropic parabolic problems

Thomas Blanc; Mihaï Bostan

doi:10.3934/dcdsb.2019186

Article Contents

2020, Volume 25, Issue 1: 335-399. Doi: 10.3934/dcdsb.2019186

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Multi-scale analysis for highly anisotropic parabolic problems

Thomas Blanc and
Mihaï Bostan^,

Aix Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille UMR 7373, Château Gombert 39 rue F. Joliot Curie, Marseille, 13453, FRANCE

^* Corresponding author: Mihaï Bostan
^* Corresponding author: Mihaï Bostan

Received: February 2018

Revised: February 2019

Early access: September 2019

Published: January 2020

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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 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.

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

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References

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