Homogenization of periodic parabolic systems in the L2(Rd)-norm with the corrector taken into account

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Homogenization of periodic parabolic systems in the L₂(R^d)-norm with the corrector taken into account. / Meshkova, Yu. M.

в: St. Petersburg Mathematical Journal, Том 31, № 4, 2020, стр. 675-718.

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

Author

Meshkova, Yu. M. / Homogenization of periodic parabolic systems in the L₂(R^d)-norm with the corrector taken into account. в: St. Petersburg Mathematical Journal. 2020 ; Том 31, № 4. стр. 675-718.

BibTeX

@article{eab5ce30e5cb4fa4bf2aa59004d7b5f2,

title = "Homogenization of periodic parabolic systems in the L2(Rd)-norm with the corrector taken into account",

abstract = "In L2(Rd;Cn), consider a selfadjoint matrix second order elliptic differential operator Bε, 0 < ε ≤ 1. The principal part of the operator is given in a factorized form, the operator contains first and zero order terms. The operator Bε is positive definite, its coefficients are periodic and depend on x/ε. The behavior in the small period limit is studied for the operator exponential. The approximation in the (L2 → L2)-operator norm with error estimate of order O(ε2) is obtained. The corrector is taken into account in this approximation. The results are applied to homogenization of the solutions for the Cauchy problem for parabolic systems.",

keywords = "Homogenization, Operator error estimates, Parabolic systems, Periodic differential operators, parabolic systems, operator error estimates, homogenization, ERROR ESTIMATE, CONVERGENCE-RATES",

author = "Meshkova, {Yu. M.}",

year = "2020",

doi = "10.1090/SPMJ/1619",

language = "English",

volume = "31",

pages = "675--718",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "4",

}

RIS

TY - JOUR

T1 - Homogenization of periodic parabolic systems in the L2(Rd)-norm with the corrector taken into account

AU - Meshkova, Yu. M.

PY - 2020

Y1 - 2020

N2 - In L2(Rd;Cn), consider a selfadjoint matrix second order elliptic differential operator Bε, 0 < ε ≤ 1. The principal part of the operator is given in a factorized form, the operator contains first and zero order terms. The operator Bε is positive definite, its coefficients are periodic and depend on x/ε. The behavior in the small period limit is studied for the operator exponential. The approximation in the (L2 → L2)-operator norm with error estimate of order O(ε2) is obtained. The corrector is taken into account in this approximation. The results are applied to homogenization of the solutions for the Cauchy problem for parabolic systems.

AB - In L2(Rd;Cn), consider a selfadjoint matrix second order elliptic differential operator Bε, 0 < ε ≤ 1. The principal part of the operator is given in a factorized form, the operator contains first and zero order terms. The operator Bε is positive definite, its coefficients are periodic and depend on x/ε. The behavior in the small period limit is studied for the operator exponential. The approximation in the (L2 → L2)-operator norm with error estimate of order O(ε2) is obtained. The corrector is taken into account in this approximation. The results are applied to homogenization of the solutions for the Cauchy problem for parabolic systems.

KW - Homogenization

KW - Operator error estimates

KW - Parabolic systems

KW - Periodic differential operators

KW - parabolic systems

KW - operator error estimates

KW - homogenization

KW - ERROR ESTIMATE

KW - CONVERGENCE-RATES

UR - http://www.scopus.com/inward/record.url?scp=85087634285&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/5c04ca02-532d-3be1-b6f3-157fcbe62765/

U2 - 10.1090/SPMJ/1619

DO - 10.1090/SPMJ/1619

M3 - Article

AN - SCOPUS:85087634285

VL - 31

SP - 675

EP - 718

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 4

ER -

ID: 62079391