July  2008, 20(3): 543-576. doi: 10.3934/dcds.2008.20.543

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, Canada, Canada

2. 

State Key Lab. of Scientific & Engin. Computing, Institute of Comput. Math. & Science-Engineering Computing, Chinese Academy of Sciences , Beijing, 100080, China

Received  November 2006 Revised  September 2007 Published  December 2007

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.
Citation: Walter Allegretto, Liqun Cao, Yanping Lin. Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 543-576. doi: 10.3934/dcds.2008.20.543
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