SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 5232-5256, January 2020.
We study increasing stability in the inverse scattering source problem for the Helmholtz equation and the classical Lamé system in the three dimensional space from boundary data at multiple wave numbers. As additional data for source identification we use pressure or displacement at the boundary of the reference domain which are natural and minimal data. By using the Fourier transform with respect to the wave numbers, explicit bounds for analytic continuation, Huygens principle, and sharp bounds for initial boundary value problems, increasing (with larger wave number intervals) stability estimates are obtained.

中文翻译：

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声学和弹性逆源问题中的稳定性提高

SIAM数学分析期刊，第52卷，第5期，第5232-5256页，2020年1月。
我们从多重波的边界数据研究三维空间中Helmholtz方程和经典Lamé系统在逆散射源问题中的稳定性。数字。作为用于源识别的其他数据，我们在参考域的边界使用压力或位移，这些压力或位移是自然数据和最小数据。通过对波数使用傅里叶变换，解析连续的显式边界，惠更斯原理以及初始边界值问题的尖锐边界，可以获得（随着更大的波数间隔）增加的稳定性估计。