American Institute of Mathematical Sciences

January  2020, 25(1): 335-399. doi: 10.3934/dcdsb.2019186

Multi-scale analysis for highly anisotropic parabolic problems

 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

Received  February 2018 Revised  February 2019 Published  September 2019

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.

Citation: Thomas Blanc, Mihaï Bostan. Multi-scale analysis for highly anisotropic parabolic problems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 335-399. doi: 10.3934/dcdsb.2019186
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