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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
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.
Received: 24.08.2023 Revised: 24.08.2023 Accepted: 05.09.2023
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
Linking options:
https://www.mathnet.ru/eng/faa4149https://doi.org/10.4213/faa4149 https://www.mathnet.ru/eng/faa/v57/i4/p123
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Abstract page: | 140 | Full-text PDF : | 3 | References: | 22 | First page: | 13 |
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