Homogenization of parabolic systems with singular perturbations

We investigate convergence rates in periodic homogenization of second-order parabolic systems with fourth-order singular perturbations. Different rates depending on $\kappa$ and $\varepsilon$, which represent respectively the strength of the singular perturbation and the scale of the heterogeneities, are obtained for the problem with Dirichlet and Navier boundary conditions.

Keywords

homogenization, convergence rate, parabolic systems, singular perturbations

2010 Mathematics Subject Classification

35B27

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This work was supported by the NSF of China (11971031) and by the NSF of Anhui Province (2108085Y01).

Received 31 January 2021

Received revised 22 February 2022

Accepted 23 February 2022

Published 29 November 2022