Uniqueness and stability for the recovery of a time-dependent source in elastodynamics

TL;DR

This paper investigates the unique determination and stability of recovering time-dependent sources in elastodynamics using boundary data, providing theoretical guarantees for inverse source problems in unbounded domains.

Contribution

It establishes uniqueness and stability results for recovering separated space-time sources in elastodynamics from boundary measurements, extending previous work to time-dependent cases.

Findings

Unique determination of spatial source from boundary data

Stability estimates for certain classes of time-dependent sources

Results applicable to unbounded domains like exterior of cavities

Abstract

This paper is concerned with inverse source problems for the time-dependent Lam\'e system in an unbounded domain corresponding to the exterior of a bounded cavity or the full space $\R^3$. If the time and spatial variables of the source term can be separated with compact support, we prove that the vector valued spatial source term can be uniquely determined by boundary Dirichlet data in the exterior of a given cavity. Uniqueness and stability for recovering some class of time-dependent source terms are also obtained using partial boundary data.