# On uniqueness of elastic scattering from a cavity

## TL;DR

This paper investigates the mathematical properties of elastic wave scattering from a cavity, establishing existence, uniqueness, and local stability results for both direct and inverse problems in elastic media.

## Contribution

It provides new theoretical results on the existence, uniqueness, and local stability of elastic scattering solutions, including analysis of Fréchet derivatives for inverse problems.

## Key findings

- Existence and uniqueness for direct elastic scattering problems.
- Local stability results for inverse scattering with Dirichlet boundary conditions.
- Analysis of Fréchet derivatives for inverse problem sensitivity.

## Abstract

The paper considers direct and inverse elastic scattering from a cavity in homogeneous medium with Dirichlet and Neumann boundary conditions. For direct scattering, existence and uniqueness are derived by variation approach. For inverse scattering, Fr$\acute{\rm e}$chet derivatives of the solution operators are investigated, which give local stability for Dirichlet case.