Multi-scale analysis for highly anisotropic parabolic problems
Thomas Blanc, Mihaï Bostan · Discrete and Continuous Dynamical Systems - B · 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.