Analysis and computation of an inverse source problem for the biharmonic wave equation

Abstract

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating 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 the Fourier series expansion by multi-wavenumber boundary measurements. The stability of the proposed method is analyzed and numerical experiments are presented to verify the accuracy and efficiency.