On homogenization of the first initial-boundary value problem for periodic hyperbolic systems

Standard

On homogenization of the first initial-boundary value problem for periodic hyperbolic systems. / Мешкова, Юлия Михайловна.

в: Applicable Analysis, Том 99, № 9, 03.07.2020, стр. 1528-1563.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Author

Мешкова, Юлия Михайловна. / On homogenization of the first initial-boundary value problem for periodic hyperbolic systems. в: Applicable Analysis. 2020 ; Том 99, № 9. стр. 1528-1563.

BibTeX

@article{6032eec9cb8349db80ceb74d2ba70b4d,

title = "On homogenization of the first initial-boundary value problem for periodic hyperbolic systems",

abstract = "Let (Formula presented.) be a bounded domain of class (Formula presented.). In (Formula presented.), we consider a self-adjoint matrix strongly elliptic second-order differential operator (Formula presented.), (Formula presented.), with the Dirichlet boundary condition. The coefficients of the operator (Formula presented.) are periodic and depend on (Formula presented.). We are interested in the behavior of the operators (Formula presented.) and (Formula presented.), (Formula presented.), in the small period limit. For these operators, approximations in the norm of operators acting from a certain subspace (Formula presented.) of the Sobolev space (Formula presented.) to (Formula presented.) are found. Moreover, for (Formula presented.), the approximation with the corrector in the norm of operators acting from (Formula presented.) to (Formula presented.) is obtained. The results are applied to homogenization for the solution of the first initial-boundary value problem for the hyperbolic equation (Formula presented.).",

keywords = "Grigory Panasenko, Periodic differential operators, homogenization, hyperbolic systems, operator error estimates, ERROR ESTIMATE, CAUCHY-PROBLEM, CORRECTORS, WAVE, PARABOLIC-SYSTEMS, DIRICHLET PROBLEM, ELLIPTIC-SYSTEMS, EQUATION",

author = "Мешкова, {Юлия Михайловна}",

note = "Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2020",

month = jul,

day = "3",

doi = "10.1080/00036811.2018.1540038",

language = "English",

volume = "99",

pages = "1528--1563",

journal = "Applicable Analysis",

issn = "0003-6811",

publisher = "Taylor & Francis",

number = "9",

}

RIS

TY - JOUR

T1 - On homogenization of the first initial-boundary value problem for periodic hyperbolic systems

AU - Мешкова, Юлия Михайловна

PY - 2020/7/3

Y1 - 2020/7/3

N2 - Let (Formula presented.) be a bounded domain of class (Formula presented.). In (Formula presented.), we consider a self-adjoint matrix strongly elliptic second-order differential operator (Formula presented.), (Formula presented.), with the Dirichlet boundary condition. The coefficients of the operator (Formula presented.) are periodic and depend on (Formula presented.). We are interested in the behavior of the operators (Formula presented.) and (Formula presented.), (Formula presented.), in the small period limit. For these operators, approximations in the norm of operators acting from a certain subspace (Formula presented.) of the Sobolev space (Formula presented.) to (Formula presented.) are found. Moreover, for (Formula presented.), the approximation with the corrector in the norm of operators acting from (Formula presented.) to (Formula presented.) is obtained. The results are applied to homogenization for the solution of the first initial-boundary value problem for the hyperbolic equation (Formula presented.).

AB - Let (Formula presented.) be a bounded domain of class (Formula presented.). In (Formula presented.), we consider a self-adjoint matrix strongly elliptic second-order differential operator (Formula presented.), (Formula presented.), with the Dirichlet boundary condition. The coefficients of the operator (Formula presented.) are periodic and depend on (Formula presented.). We are interested in the behavior of the operators (Formula presented.) and (Formula presented.), (Formula presented.), in the small period limit. For these operators, approximations in the norm of operators acting from a certain subspace (Formula presented.) of the Sobolev space (Formula presented.) to (Formula presented.) are found. Moreover, for (Formula presented.), the approximation with the corrector in the norm of operators acting from (Formula presented.) to (Formula presented.) is obtained. The results are applied to homogenization for the solution of the first initial-boundary value problem for the hyperbolic equation (Formula presented.).

KW - Grigory Panasenko

KW - Periodic differential operators

KW - homogenization

KW - hyperbolic systems

KW - operator error estimates

KW - ERROR ESTIMATE

KW - CAUCHY-PROBLEM

KW - CORRECTORS

KW - WAVE

KW - PARABOLIC-SYSTEMS

KW - DIRICHLET PROBLEM

KW - ELLIPTIC-SYSTEMS

KW - EQUATION

UR - http://www.scopus.com/inward/record.url?scp=85057541262&partnerID=8YFLogxK

UR - https://www.tandfonline.com/doi/full/10.1080/00036811.2018.1540038

UR - http://www.mendeley.com/research/homogenization-first-initialboundary-value-problem-periodic-hyperbolic-systems

U2 - 10.1080/00036811.2018.1540038

DO - 10.1080/00036811.2018.1540038

M3 - Article

VL - 99

SP - 1528

EP - 1563

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 9

ER -

ID: 35959514