论文标题
具有随机电势的Biharmonic波方程的逆散射
Inverse scattering for the biharmonic wave equation with a random potential
论文作者
论文摘要
我们考虑了有损培养基中二维和三维双旋次波方程的逆随机散射问题。假定电势是微局部各向同性高斯粗糙场。这项工作的主要贡献是双重的。首先，对于具有粗糙电势的第四阶Biharmonic波方程证明了独特的延续原理，并且在分布意义上确定了直接散射问题的良好性。其次，随机电势的相关强度被证明是由频带上散射场的第二矩的高频限制唯一确定的。此外，我们证明可以删除数据中的期望，并且单个实现的数据足以满足媒介无损时概率的逆问题的唯一性。
We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of the work are twofold. First, the unique continuation principle is proved for the fourth order biharmonic wave equation with rough potentials and the well-posedness of the direct scattering problem is established in the distribution sense. Second, the correlation strength of the random potential is shown to be uniquely determined by the high frequency limit of the second moment of the scattered field averaged over the frequency band. Moreover, we demonstrate that the expectation in the data can be removed and the data of a single realization is sufficient for the uniqueness of the inverse problem with probability one when the medium is lossless.
