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Funktsional'nyi Analiz i ego Prilozheniya, 2023, Volume 57, Issue 4, Pages 123–129
DOI: https://doi.org/10.4213/faa4149
(Mi faa4149)
 

This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

Homogenization of hyperbolic equations: operator estimates with correctors taken into account

M. A. Dorodnyi, T. A. Suslina

Saint Petersburg State University
References:
Abstract: An elliptic second-order differential operator $A_\varepsilon=b(\mathbf{D})^*g(\mathbf{x}/\varepsilon)b(\mathbf{D})$ on $L_2(\mathbb{R}^d)$ is considered, where $\varepsilon >0$, $g(\mathbf{x})$ is a positive definite and bounded matrix-valued function periodic with respect to some lattice, and $b(\mathbf{D})$ is a matrix first-order differential operator. Approximations for small $\varepsilon$ of the operator-functions $\cos(\tau A_\varepsilon^{1/2})$ and $A_\varepsilon^{-1/2} \sin (\tau A_\varepsilon^{1/2})$ in various operator norms are obtained. The results can be applied to study the behavior of the solution of the Cauchy problem for the hyperbolic equation $\partial^2_\tau \mathbf{u}_\varepsilon(\mathbf{x},\tau) = - A_\varepsilon \mathbf{u}_\varepsilon(\mathbf{x},\tau)$.
Keywords: periodic differential operators, homogenization, hyperbolic equations, operator error estimates.
Funding agency Grant number
Russian Science Foundation 22-11-00092
Received: 24.08.2023
Revised: 24.08.2023
Accepted: 05.09.2023
English version:
Functional Analysis and Its Applications, 2023, Volume 57, Issue 4, Pages 364–370
DOI: https://doi.org/10.1134/S0016266323040093
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. A. Dorodnyi, T. A. Suslina, “Homogenization of hyperbolic equations: operator estimates with correctors taken into account”, Funktsional. Anal. i Prilozhen., 57:4 (2023), 123–129; Funct. Anal. Appl., 57:4 (2023), 364–370
Citation in format AMSBIB
\Bibitem{DorSus23}
\by M.~A.~Dorodnyi, T.~A.~Suslina
\paper Homogenization of hyperbolic equations: operator estimates with correctors taken into account
\jour Funktsional. Anal. i Prilozhen.
\yr 2023
\vol 57
\issue 4
\pages 123--129
\mathnet{http://mi.mathnet.ru/faa4149}
\crossref{https://doi.org/10.4213/faa4149}
\transl
\jour Funct. Anal. Appl.
\yr 2023
\vol 57
\issue 4
\pages 364--370
\crossref{https://doi.org/10.1134/S0016266323040093}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85189096305}
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  • https://www.mathnet.ru/eng/faa4149
  • https://doi.org/10.4213/faa4149
  • https://www.mathnet.ru/eng/faa/v57/i4/p123
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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    References:22
    First page:13
     
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