WIAS Preprint No. 2524, (2018)

Temporal homogenization of a nonlinear parabolic system



Authors

  • Yu, Jie
  • Hömberg, Dietmar
  • Petzold, Thomas
  • Lu, Shuai

2010 Mathematics Subject Classification

  • 35B27 78M40 80M40

Keywords

  • Multiscale, temporal homogenization, Joule heating

DOI

10.20347/WIAS.PREPRINT.2524

Abstract

In this paper we develop are two-scale model for a nonlinear parabolic system. Assuming a rapidly oscillating inhomogeneity with period ε for one equation we carry out a formal periodic expansion to obtain a homogenized equation coupled to a local in time cell problem. We justify the expansion by deriving an error estimate between the original and the two-scale model and show numerical simulations, which confirm the analytically derived error estimate.

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