论文标题
固定角度反向散射在riemannian公制的情况下
Fixed angle inverse scattering in the presence of a Riemannian metric
论文作者
论文摘要
在存在已知的riemannian度量的情况下，我们考虑了一个固定角度反向散射问题。首先，假设没有苛刻的条件，我们通过利用进步波扩展来研究直接问题。在公制上的对称性假设下，我们获得了唯一性和稳定性导致反向散射问题，从而具有从相反方向的两个入射波产生的数据的潜力。此外，使用一个测量值给出了类似的结果，只要电势还满足对称性假设。这项工作将[23,24]的结果从欧几里得案例扩展到某些Riemannian指标。
We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption on the metric, we obtain uniqueness and stability results in the inverse scattering problem for a potential with data generated by two incident waves from opposite directions. Further, similar results are given using one measurement provided the potential also satisfies a symmetry assumption. This work extends the results of [23,24] from the Euclidean case to certain Riemannian metrics.
