Standard

Homogenization of parabolic and elliptic periodic operators in L2(ℝd) with the first and second correctors taken into account. / Vasilevskaya, E.S.; Suslina, T.A.

в: St. Petersburg Mathematical Journal, Том 24, № 2, 2013, стр. 185-261.

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Harvard

Vasilevskaya, ES & Suslina, TA 2013, 'Homogenization of parabolic and elliptic periodic operators in L2(ℝd) with the first and second correctors taken into account', St. Petersburg Mathematical Journal, Том. 24, № 2, стр. 185-261. https://doi.org/10.1090/S1061-0022-2013-01236-2

APA

Vasilevskaya, E. S., & Suslina, T. A. (2013). Homogenization of parabolic and elliptic periodic operators in L2(ℝd) with the first and second correctors taken into account. St. Petersburg Mathematical Journal, 24(2), 185-261. https://doi.org/10.1090/S1061-0022-2013-01236-2

Vancouver

Vasilevskaya ES, Suslina TA. Homogenization of parabolic and elliptic periodic operators in L2(ℝd) with the first and second correctors taken into account. St. Petersburg Mathematical Journal. 2013;24(2):185-261. https://doi.org/10.1090/S1061-0022-2013-01236-2

Author

Vasilevskaya, E.S. ; Suslina, T.A. / Homogenization of parabolic and elliptic periodic operators in L2(ℝd) with the first and second correctors taken into account. в: St. Petersburg Mathematical Journal. 2013 ; Том 24, № 2. стр. 185-261.

BibTeX

@article{73d506dda1c8432982ce914f7ba14620,
title = "Homogenization of parabolic and elliptic periodic operators in L2(ℝd) with the first and second correctors taken into account",
abstract = "In the space L2(ℝd;ℂn), a wide class of matrix elliptic second order differential operators (DO's) Aε( is studied; the A( are assumed to admit a factorization of the form A( = X* ε Xε where Xε is a homogeneous first order DO. The coefficients of these operators are periodic and depend on x/ε ,ε > 0. The behavior of the operator exponential e-A ετ > 0, and of the resolvent (Aε + I)-1 for small ε is investigated. An approximation for the exponential e-A ετ in the operator norm in L2(Rd;Cn) with an error term of order τ-3/2ε3 is obtained. For the resolvent (Aε + I)-1, approximation in the norm of operators acting from H1(ℝd;ℂn) to L2(ℝd;ℂn) is found with an error term of order ε3. In these approximations, the first and second order correctors are taken into account. {\textcopyright} 2013 American Mathematical Society.",
author = "E.S. Vasilevskaya and T.A. Suslina",
year = "2013",
doi = "10.1090/S1061-0022-2013-01236-2",
language = "English",
volume = "24",
pages = "185--261",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "2",

}

RIS

TY - JOUR

T1 - Homogenization of parabolic and elliptic periodic operators in L2(ℝd) with the first and second correctors taken into account

AU - Vasilevskaya, E.S.

AU - Suslina, T.A.

PY - 2013

Y1 - 2013

N2 - In the space L2(ℝd;ℂn), a wide class of matrix elliptic second order differential operators (DO's) Aε( is studied; the A( are assumed to admit a factorization of the form A( = X* ε Xε where Xε is a homogeneous first order DO. The coefficients of these operators are periodic and depend on x/ε ,ε > 0. The behavior of the operator exponential e-A ετ > 0, and of the resolvent (Aε + I)-1 for small ε is investigated. An approximation for the exponential e-A ετ in the operator norm in L2(Rd;Cn) with an error term of order τ-3/2ε3 is obtained. For the resolvent (Aε + I)-1, approximation in the norm of operators acting from H1(ℝd;ℂn) to L2(ℝd;ℂn) is found with an error term of order ε3. In these approximations, the first and second order correctors are taken into account. © 2013 American Mathematical Society.

AB - In the space L2(ℝd;ℂn), a wide class of matrix elliptic second order differential operators (DO's) Aε( is studied; the A( are assumed to admit a factorization of the form A( = X* ε Xε where Xε is a homogeneous first order DO. The coefficients of these operators are periodic and depend on x/ε ,ε > 0. The behavior of the operator exponential e-A ετ > 0, and of the resolvent (Aε + I)-1 for small ε is investigated. An approximation for the exponential e-A ετ in the operator norm in L2(Rd;Cn) with an error term of order τ-3/2ε3 is obtained. For the resolvent (Aε + I)-1, approximation in the norm of operators acting from H1(ℝd;ℂn) to L2(ℝd;ℂn) is found with an error term of order ε3. In these approximations, the first and second order correctors are taken into account. © 2013 American Mathematical Society.

U2 - 10.1090/S1061-0022-2013-01236-2

DO - 10.1090/S1061-0022-2013-01236-2

M3 - Article

VL - 24

SP - 185

EP - 261

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 7377339