Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients

Walter Allegretto; Liqun Cao; Yanping Lin

doi:10.3934/dcds.2008.20.543

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2008, Volume 20, Issue 3: 543-576. Doi: 10.3934/dcds.2008.20.543

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Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients

1.
Department of Mathematics and Statistics, University of Alberta, Edmonton, Alberta T6G 2G1
2.
State Key Lab. of Scientific & Engin. Computing, Institute of Comput. Math. & Science-Engineering Computing, Chinese Academy of Sciences , Beijing, 100080

Received: October 31, 2006

Revised: August 31, 2007

Published: August 2008

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Abstract

In this paper we discuss initial-boundary problems for second order parabolic equations with rapidly oscillating coefficients in a bounded convex domain. The asymptotic expansions of the solutions for problems with multiple spatial and temporal scales are presented in four different cases. Higher order corrector methods are constructed and associated explicit convergence rates obtained.

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Mathematics Subject Classification: Primary: 65F10, 35B50.

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