Standard

Homogenization of the first initial boundary-value problem for parabolic systems : Operator error estimates. / Meshkova, Yu. M.; Suslina, T. A.

в: St. Petersburg Mathematical Journal, Том 29, № 6, 01.01.2018, стр. 935-978.

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

Harvard

Meshkova, YM & Suslina, TA 2018, 'Homogenization of the first initial boundary-value problem for parabolic systems: Operator error estimates', St. Petersburg Mathematical Journal, Том. 29, № 6, стр. 935-978. https://doi.org/10.1090/spmj/1521

APA

Meshkova, Y. M., & Suslina, T. A. (2018). Homogenization of the first initial boundary-value problem for parabolic systems: Operator error estimates. St. Petersburg Mathematical Journal, 29(6), 935-978. https://doi.org/10.1090/spmj/1521

Vancouver

Meshkova YM, Suslina TA. Homogenization of the first initial boundary-value problem for parabolic systems: Operator error estimates. St. Petersburg Mathematical Journal. 2018 Янв. 1;29(6):935-978. https://doi.org/10.1090/spmj/1521

Author

Meshkova, Yu. M. ; Suslina, T. A. / Homogenization of the first initial boundary-value problem for parabolic systems : Operator error estimates. в: St. Petersburg Mathematical Journal. 2018 ; Том 29, № 6. стр. 935-978.

BibTeX

@article{3eb7412f84504894820337351109a0bf,
title = "Homogenization of the first initial boundary-value problem for parabolic systems: Operator error estimates",
abstract = "Let O ⊃ ℝd be a bounded domain of class C1,1. In L2(O;n), a selfadjoint matrix second order elliptic differential operator BD,ε, 0 < ε ≤ 1, is considered with the Dirichlet boundary condition. The principal part of the operator is given in a factorized form. The operator involves first and zero order terms. The operator BD,ε is positive definite; its coefficients are periodic and depend on x/ε. The behavior of the operator exponential e -BD,εt, t > 0, is studied as ε → 0. Approximations for the exponential e -BD,εt are obtained in the operator norm on L2(O;n) and in the norm of operators acting from L2(O;n) to the Sobolev space H1(O;n). The results are applied to homogenization of solutions of the first initial boundary-value problem for parabolic systems.",
keywords = "Homogenization, Operator error estimates, Parabolic systems, Periodic differential operators, operator error estimates, PERIODIC COEFFICIENTS, R-D, CAUCHY-PROBLEM, parabolic systems, homogenization, DIRICHLET PROBLEM, ELLIPTIC-SYSTEMS, LOWER ORDER TERMS, CONVERGENCE-RATES",
author = "Meshkova, {Yu. M.} and Suslina, {T. A.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1090/spmj/1521",
language = "English",
volume = "29",
pages = "935--978",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "6",

}

RIS

TY - JOUR

T1 - Homogenization of the first initial boundary-value problem for parabolic systems

T2 - Operator error estimates

AU - Meshkova, Yu. M.

AU - Suslina, T. A.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let O ⊃ ℝd be a bounded domain of class C1,1. In L2(O;n), a selfadjoint matrix second order elliptic differential operator BD,ε, 0 < ε ≤ 1, is considered with the Dirichlet boundary condition. The principal part of the operator is given in a factorized form. The operator involves first and zero order terms. The operator BD,ε is positive definite; its coefficients are periodic and depend on x/ε. The behavior of the operator exponential e -BD,εt, t > 0, is studied as ε → 0. Approximations for the exponential e -BD,εt are obtained in the operator norm on L2(O;n) and in the norm of operators acting from L2(O;n) to the Sobolev space H1(O;n). The results are applied to homogenization of solutions of the first initial boundary-value problem for parabolic systems.

AB - Let O ⊃ ℝd be a bounded domain of class C1,1. In L2(O;n), a selfadjoint matrix second order elliptic differential operator BD,ε, 0 < ε ≤ 1, is considered with the Dirichlet boundary condition. The principal part of the operator is given in a factorized form. The operator involves first and zero order terms. The operator BD,ε is positive definite; its coefficients are periodic and depend on x/ε. The behavior of the operator exponential e -BD,εt, t > 0, is studied as ε → 0. Approximations for the exponential e -BD,εt are obtained in the operator norm on L2(O;n) and in the norm of operators acting from L2(O;n) to the Sobolev space H1(O;n). The results are applied to homogenization of solutions of the first initial boundary-value problem for parabolic systems.

KW - Homogenization

KW - Operator error estimates

KW - Parabolic systems

KW - Periodic differential operators

KW - operator error estimates

KW - PERIODIC COEFFICIENTS

KW - R-D

KW - CAUCHY-PROBLEM

KW - parabolic systems

KW - homogenization

KW - DIRICHLET PROBLEM

KW - ELLIPTIC-SYSTEMS

KW - LOWER ORDER TERMS

KW - CONVERGENCE-RATES

UR - http://www.scopus.com/inward/record.url?scp=85054406968&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=38613502

U2 - 10.1090/spmj/1521

DO - 10.1090/spmj/1521

M3 - Article

AN - SCOPUS:85054406968

VL - 29

SP - 935

EP - 978

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 6

ER -

ID: 36545065