Research output: Contribution to journal › Article › peer-review
Homogenization of the first initial boundary-value problem for parabolic systems : Operator error estimates. / Meshkova, Yu. M.; Suslina, T. A.
In: St. Petersburg Mathematical Journal, Vol. 29, No. 6, 01.01.2018, p. 935-978.Research output: Contribution to journal › Article › peer-review
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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