In this paper we study a wave equation with discontinuous principal coefficient within a bounded domain of arbitrary dimension. It is obtained the stability of the inverse problem of recovering a space-dependent coefficient by observing a trace of the corresponding solution on part of the boundary. We provide a precise estimate of the minimum required time, as a function of the velocity change and domain size. The main tools are new global Carleman estimates for the transmission system with a particular weight function adapted to the interface geometry, which allows to obtain an optimal estimate of the minimum time.

中文翻译：

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Rn 中平坦界面传输波方程的反问题

在本文中，我们研究了在任意维数有界域内具有不连续主系数的波动方程。通过观察部分边界上相应解的迹，获得了恢复空间相关系数反问题的稳定性。我们提供了最短所需时间的精确估计，作为速度变化和域大小的函数。主要工具是针对传输系统的新的全局卡尔曼估计，具有适合界面几何形状的特定权重函数，从而可以获得最短时间的最佳估计。