We are concerned with the reconstruction of a one dimensional wave equation, where the potential is known in a neighborhood of one of the end points of the boundary. We show then the sought potential can be determined by one single measurement of the solution at that end. We also show that the solution can be evaluated at the other end without the need of solving the wave the equation.

中文翻译：

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从一侧测量重建波动方程

我们关注一维波动方程的重建，其中边界端点之一的邻域内的势是已知的。我们表明，寻求的潜力可以通过对解决方案的一次单一测量来确定。我们还表明，可以在另一端评估解，而无需求解波动方程。