DOI

In L 2(R d;C n), we consider selfadjoint strongly elliptic second order differential operators A ε with periodic coefficients depending on x/ε ε>0. We study the behavior of the operators cos⁡(A ε 1/2τ) and A ε −1/2sin⁡(A ε 1/2τ), τ∈R, for small ε. Approximations for these operators in the (H s→L 2)-operator norm with a suitable s are obtained. The results are used to study the behavior of the solution v ε of the Cauchy problem for the hyperbolic equation ∂ τ 2v ε=−A εv ε+F. General results are applied to the acoustics equation and the system of elasticity theory.

Язык оригиналаанглийский
Страницы (с-по)7463-7522
Число страниц60
ЖурналJournal of Differential Equations
Том264
Номер выпуска12
DOI
СостояниеОпубликовано - 15 июн 2018

    Предметные области Scopus

  • Математика (все)
  • Анализ

ID: 35180204