2017/05/03 by Qiang Xu, Xu, Qiang, Shulin Zhou +1 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1705.01479
openalex publication_date 2017/05/03 · openalex created_date 2017/05/12 · openalex updated_date 2026/07/28
In a Lipschitz cylinder, this paper is devoted to establish an almost sharp error estimate O(εlog2(1/ε)) in L2-norm for parabolic systems of elasticity with initial-Dirichlet conditions, arising in the homogenization theory. To achieve the goal, with the parabolic distance function being a weight, we first developed some new weighted-type inequalities for the smoothing operator at scale ε in terms of t-anisotropic Sobolev spaces, and then all the problems may be reduced to three kinds of estimate for the homogenized system, in which a weighted-type Caccioppoli's inequality on time-layer has also been found. Throughout the paper, we do not introduce any smoothness on coefficients compared to the arguments investigated by C.Kenig, F. Lin and Z. Shen in \citeSZW2, while this study can be considered to be a further development of \citeGZS and \citeQX2.