论文标题
具有单个动力学数据的时间相关的逆问题的唯一性
Uniqueness for time-dependent inverse problems with single dynamical data
论文作者
论文摘要
在这项工作中，我们研究了与两个时间依赖的偏微分方程相关的形状识别和系数确定。我们考虑了确定凸多边形障碍物的逆问题，以及从单个动态数据以及时间出现在Wave和Schrödinger方程中的系数。借助远场数据，我们首先证明波动方程的声速及其对凸 - 培训类型的对比度支持可以唯一确定，然后确定恢复电势以及其在Schrödinger方程中出现的支持的唯一性结果。由于这些结果，我们证明了从单个远场模式中以固定频率从单个远场模式中恢复介质的折射率的独特性结果。
In this work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal obstacle and the coefficient appearing in the wave and Schrödinger equations from a single dynamical data along with the time. With the far field data, we first prove that the sound speed of the wave equation together with its contrast support of convex-polygon type can be uniquely determined, then establish a uniqueness result for recovering an electric potential as well as its support appearing in the Schrödinger equation. As a consequence of these results, we demonstrate a uniqueness result for recovering the refractive index of a medium from a single far field pattern at a fixed frequency in the time-harmonic regime.
