Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials

T. Chaumont-Frelet; S. Nicaise

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arXiv · 2403.07415

Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials

T. Chaumont-Frelet·S. Nicaise

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Abstract

We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $\omega$ and ratio of the Lam\'e parameters $\lambda/\mu$ may both be large. We derive stability estimates controlling the norm of the solution by the norm of the right-hand side up to a fully-explicit constant. Crucially, under natural assumptions on the domain and coefficients, this constant increases linearly with $\omega$ and is uniform in the ratio $\lambda/\mu$.

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T. Chaumont-Frelet, S. Nicaise. 2024-03-12. Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials. https://arxiv.org/abs/2403.07415

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