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Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap. / Akhmatova, A. R.; Aksenova, E. S.; Sloushch, V. A.; Suslina, T. A.

In: Complex Variables and Elliptic Equations, 08.07.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Akhmatova, AR, Aksenova, ES, Sloushch, VA & Suslina, TA 2021, 'Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap', Complex Variables and Elliptic Equations. https://doi.org/10.1080/17476933.2021.1947259, https://doi.org/10.1080/17476933.2021.1947259

APA

Akhmatova, A. R., Aksenova, E. S., Sloushch, V. A., & Suslina, T. A. (2021). Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap. Complex Variables and Elliptic Equations. https://doi.org/10.1080/17476933.2021.1947259, https://doi.org/10.1080/17476933.2021.1947259

Vancouver

Akhmatova AR, Aksenova ES, Sloushch VA, Suslina TA. Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap. Complex Variables and Elliptic Equations. 2021 Jul 8. https://doi.org/10.1080/17476933.2021.1947259, https://doi.org/10.1080/17476933.2021.1947259

Author

Akhmatova, A. R. ; Aksenova, E. S. ; Sloushch, V. A. ; Suslina, T. A. / Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap. In: Complex Variables and Elliptic Equations. 2021.

BibTeX

@article{0f0d165c7d6c4bd6941e61b6fc2b3413,
title = "Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap",
abstract = "In (Formula presented.), consider a second-order elliptic differential operator (Formula presented.), (Formula presented.), of the form (Formula presented.) with periodic coefficients. For small ε, we study the behavior of the semigroup (Formula presented.), t>0, cut by the spectral projection of the operator (Formula presented.) for the interval (Formula presented.). Here (Formula presented.) is the right edge of a spectral gap for the operator (Formula presented.). We obtain approximation for the {\textquoteleft}cut semigroup{\textquoteright} in the operator norm in (Formula presented.) with error (Formula presented.), and also a more accurate approximation with error (Formula presented.) (after singling out the factor (Formula presented.)). The results are applied to homogenization of the Cauchy problem (Formula presented.), (Formula presented.), with the initial data (Formula presented.) from a special class.",
keywords = "homogenization, operator error estimates, parabolic equation, Periodic differential operators, Primary: 35B27, spectral gap",
author = "Akhmatova, {A. R.} and Aksenova, {E. S.} and Sloushch, {V. A.} and Suslina, {T. A.}",
note = "Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2021",
month = jul,
day = "8",
doi = "10.1080/17476933.2021.1947259",
language = "English",
journal = "Complex Variables and Elliptic Equations",
issn = "1747-6933",
publisher = "Taylor & Francis",

}

RIS

TY - JOUR

T1 - Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap

AU - Akhmatova, A. R.

AU - Aksenova, E. S.

AU - Sloushch, V. A.

AU - Suslina, T. A.

N1 - Publisher Copyright: © 2021 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021/7/8

Y1 - 2021/7/8

N2 - In (Formula presented.), consider a second-order elliptic differential operator (Formula presented.), (Formula presented.), of the form (Formula presented.) with periodic coefficients. For small ε, we study the behavior of the semigroup (Formula presented.), t>0, cut by the spectral projection of the operator (Formula presented.) for the interval (Formula presented.). Here (Formula presented.) is the right edge of a spectral gap for the operator (Formula presented.). We obtain approximation for the ‘cut semigroup’ in the operator norm in (Formula presented.) with error (Formula presented.), and also a more accurate approximation with error (Formula presented.) (after singling out the factor (Formula presented.)). The results are applied to homogenization of the Cauchy problem (Formula presented.), (Formula presented.), with the initial data (Formula presented.) from a special class.

AB - In (Formula presented.), consider a second-order elliptic differential operator (Formula presented.), (Formula presented.), of the form (Formula presented.) with periodic coefficients. For small ε, we study the behavior of the semigroup (Formula presented.), t>0, cut by the spectral projection of the operator (Formula presented.) for the interval (Formula presented.). Here (Formula presented.) is the right edge of a spectral gap for the operator (Formula presented.). We obtain approximation for the ‘cut semigroup’ in the operator norm in (Formula presented.) with error (Formula presented.), and also a more accurate approximation with error (Formula presented.) (after singling out the factor (Formula presented.)). The results are applied to homogenization of the Cauchy problem (Formula presented.), (Formula presented.), with the initial data (Formula presented.) from a special class.

KW - homogenization

KW - operator error estimates

KW - parabolic equation

KW - Periodic differential operators

KW - Primary: 35B27

KW - spectral gap

UR - http://www.scopus.com/inward/record.url?scp=85110212867&partnerID=8YFLogxK

U2 - 10.1080/17476933.2021.1947259

DO - 10.1080/17476933.2021.1947259

M3 - Article

AN - SCOPUS:85110212867

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

ER -

ID: 91195585