论文标题
随机schrödinger方程的逆问题，具有未知来源和电势
Inverse problem for a random Schrödinger equation with unknown source and potential
论文作者
论文摘要
在本文中，我们研究了与时间谐波schrödinger方程相关的反向散射问题，在该方程中，电势和源术语都是未知的。源项假定为微局部各向同性类型的广义高斯随机分布，而潜在函数被认为是确定性的。向前散射问题的适应性首先是从适当的意义上确定的。然后证明，通过单一的实现被动散射测量值，可以独立地恢复随机源的粗糙强度，独立于未知电位。除了使用两个未知数的被动测量样本外，我们结果的另一个重要特征是，对源的支撑和电势没有几何限制：它们可以分离，重叠，或一个包含另一个。
In this paper, we study an inverse scattering problem associated with the time-harmonic Schrödinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random distribution of the microlocally isotropic type, whereas the potential function is assumed to be deterministic. The well-posedness of the forward scattering problem is first established in a proper sense. It is then proved that the rough strength of the random source can be uniquely recovered, independent of the unknown potential, by a single realisation of the passive scattering measurement. In addition to the use of a single sample of the passive measurement for two unknowns, another significant feature of our result is that there is no geometric restriction on the supports of the source and the potential: they can be separated, or overlapped, or one containing the other.
