Sfaxi, Mourad; Sili, Ali Correctors for parabolic equations in a heterogeneous fibered medium. (English) Zbl 1196.35041 Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 10, No. 3, bis, 1025-1053 (2007). The authors consider the problem of correctors for the homogenization of linear parabolic equations in an \(\varepsilon\)-periodic medium made of two materials having highly contrast conductivities. The key feature of this work is the study of the effect of the initial data on the asymptotic behavior of the solution as \(\varepsilon\) tends to zero. They prove that there exists a corrector of the solution such that the remaining part is a time boundary layer which is not concentrated in the initial time. Reviewer: Dan Polisevski (Bucureşti) MSC: 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 35K57 Reaction-diffusion equations 76R50 Diffusion Keywords:highly contrast conductivities; time boundary layer; periodic medium; effect of the initial data PDFBibTeX XMLCite \textit{M. Sfaxi} and \textit{A. Sili}, Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 10, No. 3, bis, 1025--1053 (2007; Zbl 1196.35041)