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Multiscale asymptotic expansion for second order parabolic equations with rapidly oscillating coefficients. (English) Zbl 1145.65067
The paper is concerned with the study of the multiscale analysis of linear parabolic equations with rapidly oscillating coefficients which depend on spatial and temporal variables. The authors present the determination of the convergence rate for the approximate solutions by using a suitable cut-off function, the definition of boundary layer solutions, and higher-order correctors. Regularity estimates for the boundary layer solutions and numerical approximations techniques are presented.

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35B50 Maximum principles in context of PDEs
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K15 Initial value problems for second-order parabolic equations