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arXiv · 2504.01769

Operator aspects of wave propagation through periodic media

Kirill Cherednichenko·Yi-Sheng Lim
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Abstract

Recent results in quantitative homogenisation of the wave equation with rapidly oscillating coefficients are discussed from the operator-theoretic perspective, which views the solution as the result of applying the operator of hyperbolic dynamics, i.e. the unitary group of a self-adjoint operator on a suitable Hilbert space. A prototype one-dimensional example of utilising the framework of Ryzhov boundary triples is analysed, where operator-norm resolvent estimates for the problem of classical moderate-contrast homogenisation are obtained. By an appropriate "dilation" procedure, these are shown to upgrade to second-order (and more generally, higher-order) estimates for the resolvent and the unitary group describing the evolution for the related wave equation.

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Kirill Cherednichenko, Yi-Sheng Lim. 2025-04-02. Operator aspects of wave propagation through periodic media. https://arxiv.org/abs/2504.01769

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