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In , we consider a selfadjoint matrix strongly elliptic second order differential operator , . The coefficients of the operator are periodic and depend on . We study the asymptotic behavior of the operator , , in the small period limit. The principal term of approximation in the -norm for this operator is found. Approximation in the -operator norm with the correction term taken into account is also established. The error estimates are of the sharp order . The results are applied to homogenization for the solutions of the hyperbolic equation . As examples, we consider the acoustics equation, the system of elasticity, and the model equation of electrodynamics.
Cite this article
Yulia M. Meshkova, On operator error estimates for homogenization of hyperbolic systems with periodic coefficients. J. Spectr. Theory 11 (2021), no. 2, pp. 587–660