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Homogenization of initial boundary value problems for parabolic systems with periodic coefficients. / Meshkova, Y.M.; Suslina, T.A.

In: Applicable Analysis, Vol. 95, No. 8, 2016, p. 1736-1775.

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Meshkova, Y.M. ; Suslina, T.A. / Homogenization of initial boundary value problems for parabolic systems with periodic coefficients. In: Applicable Analysis. 2016 ; Vol. 95, No. 8. pp. 1736-1775.

BibTeX

@article{6e3bef0907994e28ae96e680d17ceaba,
title = "Homogenization of initial boundary value problems for parabolic systems with periodic coefficients",
abstract = "{\textcopyright} 2015 Taylor & Francis Let (Formula presented.) be a bounded domain of class (Formula presented.). In the Hilbert space (Formula presented.), we consider matrix elliptic second-order differential operators (Formula presented.) and (Formula presented.) with the Dirichlet or Neumann boundary condition on (Formula presented.), respectively. Here (Formula presented.) is the small parameter. The coefficients of the operators are periodic and depend on (Formula presented.). The behaviour of the operator (Formula presented.), (Formula presented.), for small (Formula presented.) is studied. It is shown that, for fixed (Formula presented.), the operator (Formula presented.) converges in the (Formula presented.)-operator norm to (Formula presented.), as (Formula presented.). Here (Formula presented.) is the effective operator with constant coefficients. For the norm of the difference of the operators (Formula presented.) and (Formula presented.), a sharp order estimate (of order (Formula presented.)) is obtained. Also",
author = "Y.M. Meshkova and T.A. Suslina",
year = "2016",
doi = "10.1080/00036811.2015.1068300",
language = "English",
volume = "95",
pages = "1736--1775",
journal = "Applicable Analysis",
issn = "0003-6811",
publisher = "Taylor & Francis",
number = "8",

}

RIS

TY - JOUR

T1 - Homogenization of initial boundary value problems for parabolic systems with periodic coefficients

AU - Meshkova, Y.M.

AU - Suslina, T.A.

PY - 2016

Y1 - 2016

N2 - © 2015 Taylor & Francis Let (Formula presented.) be a bounded domain of class (Formula presented.). In the Hilbert space (Formula presented.), we consider matrix elliptic second-order differential operators (Formula presented.) and (Formula presented.) with the Dirichlet or Neumann boundary condition on (Formula presented.), respectively. Here (Formula presented.) is the small parameter. The coefficients of the operators are periodic and depend on (Formula presented.). The behaviour of the operator (Formula presented.), (Formula presented.), for small (Formula presented.) is studied. It is shown that, for fixed (Formula presented.), the operator (Formula presented.) converges in the (Formula presented.)-operator norm to (Formula presented.), as (Formula presented.). Here (Formula presented.) is the effective operator with constant coefficients. For the norm of the difference of the operators (Formula presented.) and (Formula presented.), a sharp order estimate (of order (Formula presented.)) is obtained. Also

AB - © 2015 Taylor & Francis Let (Formula presented.) be a bounded domain of class (Formula presented.). In the Hilbert space (Formula presented.), we consider matrix elliptic second-order differential operators (Formula presented.) and (Formula presented.) with the Dirichlet or Neumann boundary condition on (Formula presented.), respectively. Here (Formula presented.) is the small parameter. The coefficients of the operators are periodic and depend on (Formula presented.). The behaviour of the operator (Formula presented.), (Formula presented.), for small (Formula presented.) is studied. It is shown that, for fixed (Formula presented.), the operator (Formula presented.) converges in the (Formula presented.)-operator norm to (Formula presented.), as (Formula presented.). Here (Formula presented.) is the effective operator with constant coefficients. For the norm of the difference of the operators (Formula presented.) and (Formula presented.), a sharp order estimate (of order (Formula presented.)) is obtained. Also

U2 - 10.1080/00036811.2015.1068300

DO - 10.1080/00036811.2015.1068300

M3 - Article

VL - 95

SP - 1736

EP - 1775

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 8

ER -

ID: 7546714