# Recovery of a fast oscillating source in the heat equation by asymptotic of the solution

## TL;DR

This paper demonstrates that a high-frequency source in a 1D heat equation can be fully recovered using partial asymptotic data of the solution, with the authors providing asymptotic analysis and solution reconstruction methods.

## Contribution

The paper introduces a novel approach to recover high-frequency sources in the heat equation using incomplete asymptotic information of the solution.

## Key findings

- Source can be recovered from two-term asymptotic data
- Asymptotic solutions are constructed and justified for the original problem
- Method applies to multiple recovery problems in heat equations

## Abstract

Four problems about recovery of a high-frequency source in the one-dimension heat equation with homogeneous initial-boundary conditions by some information about partial asymptotic of its solution have solved. It is shown, that the source can be completely recovered from a specific data about incomplete (two-terms) asymptotic of the solution. Before formulation of each problem about recovery of a source, construction and justification of the asymptotic of the solution of original initial-boundary problem is given.