发表机构
National Chengchi University; University of Jyväskylä; KTH Royal Institute of Technology（国立政治大学; 于韦斯屈莱大学; 皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究弹性波在角域中的散射，证明具有角或边缘奇异性的可穿透障碍物会散射所有满足条件的入射波，将标量结果推广到方程组，确立“角总是散射”原理。
AI 中文摘要
我们研究了在固定波数下，弹性波在各向异性非均匀介质中的散射问题。我们证明了在二维空间中，每个具有分段C^1边界和角奇异性的可穿透障碍物，以及在更高维度中，每个具有边缘奇异性的障碍物，都会散射满足适当假设的每个入射波。这项工作将我们之前的结果[J. Math. Anal. Appl. 2026, doi: https://doi.org/10.1016/j.jmaa.2026.130630]从标量方程推广到方程组，这一推广需要更精细的爆破分析和更复杂的计算。粗略地说，我们的结果确立了“角总是散射”的原理，适用于具有变系数的各向异性介质。
英文摘要
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.
Comments28 pages
