# The reconstruction of a wave equation from one side measurement

## TL;DR

This paper demonstrates that the potential in a one-dimensional wave equation can be reconstructed from a single boundary measurement, and the solution at the opposite boundary can be obtained without solving the wave equation.

## Contribution

It introduces a method to reconstruct the potential from one boundary measurement and evaluate the solution at the other boundary without solving the wave equation.

## Key findings

- Potential can be reconstructed from one boundary measurement.
- Solution at the opposite boundary can be evaluated directly.
- Reconstruction does not require solving the wave equation.

## Abstract

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.