In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into a radiating source and a non-radiating source. The radiating source can be uniquely determined by Dirichlet boundary measurements at a fixed wavenumber. Moreover, we derive a Lipschitz stability estimate for determining the radiating source. On the other hand, the non-radiating source does not produce any scattered fields outside the support of the source function. Numerically, we propose a novel source reconstruction method based on Fourier series expansion by multi-wavenumber boundary measurements. Numerical experiments are presented to verify the accuracy and efficiency of the proposed method.

翻译：本文研究双调和波动方程的反源问题。在数学上，我们刻画了固定波数下的辐射源与非辐射源。研究表明，一般源可分解为辐射源与非辐射源两部分，其中辐射源可通过固定波数下的Dirichlet边界测量唯一确定。此外，我们推导了确定辐射源的Lipschitz稳定性估计。另一方面，非辐射源在源函数支撑区域外不会产生任何散射场。在数值方法层面，我们提出了一种基于多波数边界测量的Fourier级数展开的源重建新方法。数值实验验证了所提方法的准确性与高效性。