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

Guanghui Hu, Yavar Kian

Published 2018-10-23Version 1

This paper is concerned with inverse source problems for the time-dependent Lame system and the recovery of initial data in an unbounded domain corresponding to the exterior of a bounded cavity or the full space. 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. If the cavity is absent, uniqueness and stability for recovering source terms depending on the time variable and two spatial variables in the whole space are also obtained using partial Dirichlet boundary data.