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arXiv · 2504.10629

Spectral properties of operators and wave propagation in high-contrast media

Yuri A. Godin·Leonid Koralov·Boris Vainberg
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Abstract

The paper aims to study the spectral properties of elliptic operators with highly inhomogeneous coefficients and related issues concerning wave propagation in high-contrast media. A unified approach to solving problems in bounded domains with Dirichlet or Neumann boundary conditions, as well as in infinite periodic media, is proposed. For a small parameter $\varepsilon > 0$ characterizing the contrast of the components of the medium, the analyticity of the eigenvalues and eigenfunctions is established in a neighborhood of $\varepsilon = 0$. Effective operators corresponding to $\varepsilon = 0$ are described.

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Yuri A. Godin, Leonid Koralov, Boris Vainberg. 2025-04-14. Spectral properties of operators and wave propagation in high-contrast media. https://arxiv.org/abs/2504.10629

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