On operator error estimates for homogenization of hyperbolic systems with periodic coefficients

2017/05/06 by Meshkova, Yulia
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.02531

Abstract

In L₂(ℝ^d;ℂⁿ), we consider a selfadjoint matrix strongly elliptic second order differential operator A_ε, ε >0. The coefficients of the operator A_ε are periodic and depend on x/ε. We study the behavior of the operator A_ε ^-1/2sin (τA_ε ^1/2), τ∈ℝ, in the small period limit. The principal term of approximation in the (H¹→ L₂)-norm for this operator is found. Approximation in the (H²→ H¹)-operator norm with the correction term taken into account is also established. The results are applied to homogenization for the solutions of the nonhomogeneous hyperbolic equation ∂ ²_τu_ε =-A_ε u_ε +F.

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