Fixed angle inverse scattering in the presence of a Riemannian metric
Fixed angle inverse scattering in the presence of a Riemannian metric
复制标题
存在黎曼度量时的固定角度逆散射
DOI：
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发表时间：
2020
影响因子：
1.1
通讯作者：
M. Salo
中科院分区：
文献类型：
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作者：
Shiqi Ma;M. Salo
摘要考虑了已知黎曼度规存在下的定角逆散射问题。首先，在无焦散的条件下，利用级数波展开研究了直接问题。在度量的对称假设下，我们得到了由两个相反方向入射波产生数据的势能逆散射问题的唯一性和稳定性结果。此外，如果势也满足对称假设，则使用一次测量可以得到类似的结果。这项工作扩展了Rakesh和M. Salo的结果，几乎对称或控制扰动的固定角度逆散射，SIAM J. Math。[j]和[Rakesh， M. Salo，固定角散射问题和双测量波动方程反演问题，反演问题36 2020,3，文章ID 035005]从欧氏情况到某些黎曼度量。
Abstract 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 [Rakesh and M. Salo, Fixed angle inverse scattering for almost symmetric or controlled perturbations, SIAM J. Math. Anal. 52 2020, 6, 5467–5499] and [Rakesh and M. Salo, The fixed angle scattering problem and wave equation inverse problems with two measurements, Inverse Problems 36 2020, 3, Article ID 035005] from the Euclidean case to certain Riemannian metrics.