Homogenization of Parabolic Equations with Non-self-similar Scales

Jun Geng; Zhongwei Shen

doi:10.1007/s00205-019-01467-5

Homogenization of Parabolic Equations with Non-self-similar Scales

Jun Geng, Zhongwei Shen

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Abstract

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 C¹ ^, ^α and C² ^, ^α estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems.

Original language	English
Pages (from-to)	145-188
Number of pages	44
Journal	Archive for Rational Mechanics and Analysis
Volume	236
Issue number	1
DOIs	https://doi.org/10.1007/s00205-019-01467-5
State	Published - Apr 1 2020

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Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-019-01467-5

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abstract = "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 C1 , α and C2 , α estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems.",

author = "Jun Geng and Zhongwei Shen",

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AB - 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 C1 , α and C2 , α estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems.

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Homogenization of Parabolic Equations with Non-self-similar Scales

Abstract

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