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

Pages: 543 - 576, Volume 20, Issue 3, March 2008

doi:10.3934/dcds.2008.20.543       Abstract        Full Text (399.5K)       Related Articles

Walter Allegretto - Department of Mathematics and Statistics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada (email)
Liqun Cao - State Key Lab. of Scientific & Engin. Computing, Institute of Comput. Math. & Science-Engineering Computing, Chinese Academy of Sciences , Beijing, 100080, China (email)
Yanping Lin - Department of Mathematics and Statistics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada (email)

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.

Keywords:  Homogenization, asymptotic expansion, parabolic equation with rapidly oscillating coefficients, boundary layer, finite element method, linear system of differential equation with real periodic coefficients.
Mathematics Subject Classification:  Primary: 65F10, 35B50.

Received: November 2006;      Revised: September 2007;      Published: December 2007.