具有点源的波动方程系数逆问题的持子稳定性估计

Pub Date : 2022-06-28 DOI:10.32523/2306-6172-2022-10-2-11-25

M. Klibanov, V. Romanov

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引用次数: 1

摘要

我们考虑了具有反向散射非超定数据的类波动方程的三维系数反问题。正演问题是Cauchy问题，其初始条件为集中在点源的单个位置的delta函数。我们将原问题简化为一个关于三个空间变量中的两个空间变量的有限差分问题，并研究了它的一个逆问题。

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A HOLDER STABILITY ESTIMATE FOR A COEFFICIENT ̈ INVERSE PROBLEM FOR THE WAVE EQUATION WITH A POINT SOURCE

We consider a 3D coefficient inverse problem for the wave-like equation with backscattering non-overdetermined data. The forward problem is the Cauchy problem with the initial condition as the delta-function concentrated at a single location of the point source. We reduce the original problem to a problem with finite differences with respect to two out of three spatial variables and study an inverse problem for it. A stability estimate is stated for this reduced inverse problem.

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