# Recovery of a fast oscillating free term in the wave equation by asymptotics of the solution

## TL;DR

This paper demonstrates that a high-frequency free term in a 1D wave equation can be fully recovered using partial asymptotic data of the solution, advancing inverse problem techniques.

## Contribution

It introduces methods to recover a high-frequency free term from incomplete asymptotic information of the wave solution, with rigorous asymptotic analysis.

## Key findings

- Complete recovery of the free term from three-term asymptotics
- Construction and justification of solution asymptotics
- Application to inverse problems in wave equations

## Abstract

Three problems about recovery of a high-frequency free term in the one-dimension wave equation with homogeneous initial-boundary conditions by some information about partial asymptotics of its solution have been solved. It is shoun, that the free term can be completely recovered from a specific data about incomplete (three-terms) asymptotics of the solution. Before formulation of the each problem about recovery of free term, construction and justification of the asymptotics of the solution of original initial-boundary problem are given.