Spectral approach to homogenization of hyperbolic equations with periodic coefficients
Dorodnyi, Mark · Suslina, Tatiana
Original · EN
In L₂(Rᵈ;Cⁿ), we consider selfadjoint strongly elliptic second order differential operators Aε with periodic coefficients depending on x/ ε, ε>0. We study the behavior of the operators (A¹/²ε τ) and A⁻¹/²ε (A¹/²ε τ), τ∈ R, for small ε. Approximations for these operators in the (Hˢ→ L₂)-operator norm with a suitable s are obtained. The results are used to study the behavior of the solution vε of the Cauchy problem for the hyperbolic equation ∂²τvε = - Aε vε +F. General results are applied to the acoustics equation and the system of elasticity theory.
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