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arXiv · 2212.10206

A high-contrast composite with annular inclusions: Norm-resolvent asymptotics

Yi-Sheng Lim
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Abstract

We investigate the operator-norm resolvent asymptotics of a high-contrast composite, consisting of a "stiff" material, with annular "soft" inclusions (a "stiff-soft-stiff" setup). This setup is derived from two models with very different effective wave propagation behaviors. Our analysis is based on an operator-framework proposed by Cherednichenko, Ershova, and Kiselev in [Effective Behaviour of Critical-Contrast PDEs: Micro-resonances, Frequency Conversion, and Time Dispersive Properties. I. Commun. Math. Phys. 375, p. 1833-1884]. Then, as a first step towards studying wave propagation on the stiff-soft-stiff composite, we use the effective description to derive analogous "dispersion functions".

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Yi-Sheng Lim. 2023-11-01. A high-contrast composite with annular inclusions: Norm-resolvent asymptotics. https://arxiv.org/abs/2212.10206

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