Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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 оригинала | английский |
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Страницы (с-по) | 7463-7522 |
Число страниц | 60 |
Журнал | Journal of Differential Equations |
Том | 264 |
Номер выпуска | 12 |
DOI | |
Состояние | Опубликовано - 15 июн 2018 |
ID: 35180204