Homogenization of Parabolic Equations with Non-self-similar Scales

  • Jun Geng
  • Zhongwei ShenEmail author


This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in non-self-similar scales. The homogenization problem involves two oscillating scales. We obtain large-scale interior and boundary Lipschitz estimates as well as interior \(C^{1, \alpha }\) and \(C^{2, \alpha }\) estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems.

Mathematics Subject Classification

35B27 35K40 



Both authors thank the anonymous referees for their very helpful comments, corrections, and suggestions.

Compliance with ethical standards

Conflict of interest

Authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA

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