PreprintarXiv licencearXiv
On elastic scattering behavior of corner domains
Abstract
We investigate the scattering of elastic waves by anisotropic inhomogeneous media at a fixed wave number. We prove that, in two dimensions, every penetrable obstacle with piecewise C1 boundary and corner singularities, and, in higher dimensions, every obstacle with edge singularities, scatters every incident wave satisfying suitable assumptions. This work extends our previous result [J. Math. Anal. Appl. 2026, doi:10.1016/j.jmaa.2026.130630] from scalar equations to systems of equations, a generalization that requires a more delicate blowup analysis and more involved computations. Roughly speaking, our results establish the principle that \emph{corners always scatter} for general anisotropic media with variable coefficients.
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BibTeX
@misc{kow2026elastic,
title = {{On elastic scattering behavior of corner domains}},
author = {Pu-Zhao Kow and Mikko Salo and Henrik Shahgholian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32148},
eprint = {2609.32148},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32148},
}
RIS
TY - UNPB
TI - On elastic scattering behavior of corner domains
AU - Pu-Zhao Kow
AU - Mikko Salo
AU - Henrik Shahgholian
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32148
UR - https://arxiv.org/abs/2609.32148
AB - We investigate the scattering of elastic waves by anisotropic inhomogeneous media at a fixed wave number. We prove that, in two dimensions, every penetrable obstacle with piecewise C^1 boundary and corner singularities, and, in higher dimensions, every obstacle with edge singularities, scatters every incident wave satisfying suitable assumptions. This work extends our previous result [J. Math. Anal. Appl. 2026, doi:10.1016/j.jmaa.2026.130630] from scalar equations to systems of equations, a generalization that requires a more delicate blowup analysis and more involved computations. Roughly speaking, our results establish the principle that \emph{corners always scatter} for general anisotropic media with variable coefficients.
ER -