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Spectral approach to homogenization of hyperbolic equations with periodic coefficients. / Дородный, Марк Александрович; Суслина, Татьяна Александровна.

In: Journal of Differential Equations, Vol. 264, No. 12, 15.06.2018, p. 7463-7522.

Research output: Contribution to journal › Article › peer-review

Harvard

Дородный, МА & Суслина, ТА 2018, 'Spectral approach to homogenization of hyperbolic equations with periodic coefficients', Journal of Differential Equations, vol. 264, no. 12, pp. 7463-7522. https://doi.org/10.1016/j.jde.2018.02.023

APA

Дородный, М. А., & Суслина, Т. А. (2018). Spectral approach to homogenization of hyperbolic equations with periodic coefficients. Journal of Differential Equations, 264(12), 7463-7522. https://doi.org/10.1016/j.jde.2018.02.023

Vancouver

Дородный МА, Суслина ТА. Spectral approach to homogenization of hyperbolic equations with periodic coefficients. Journal of Differential Equations. 2018 Jun 15;264(12):7463-7522. https://doi.org/10.1016/j.jde.2018.02.023

Author

Дородный, Марк Александрович ; Суслина, Татьяна Александровна. / Spectral approach to homogenization of hyperbolic equations with periodic coefficients. In: Journal of Differential Equations. 2018 ; Vol. 264, No. 12. pp. 7463-7522.

BibTeX

@article{2a395fc6b11e47b488dce3092ab5b328,
title = "Spectral approach to homogenization of hyperbolic equations with periodic coefficients",
abstract = "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. ",
keywords = "Effective operator, Homogenization, Hyperbolic equations, Operator error estimates, Periodic differential operators",
author = "Дородный, {Марк Александрович} and Суслина, {Татьяна Александровна}",
year = "2018",
month = jun,
day = "15",
doi = "10.1016/j.jde.2018.02.023",
language = "English",
volume = "264",
pages = "7463--7522",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Elsevier",
number = "12",

}

RIS

TY - JOUR

T1 - Spectral approach to homogenization of hyperbolic equations with periodic coefficients

AU - Дородный, Марк Александрович

AU - Суслина, Татьяна Александровна

PY - 2018/6/15

Y1 - 2018/6/15

N2 - 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.

AB - 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.

KW - Effective operator

KW - Homogenization

KW - Hyperbolic equations

KW - Operator error estimates

KW - Periodic differential operators

UR - http://www.scopus.com/inward/record.url?scp=85042395446&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2018.02.023

DO - 10.1016/j.jde.2018.02.023

M3 - Article

VL - 264

SP - 7463

EP - 7522

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 12

ER -

ID: 35180204