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

Guanghui Hu (1) , Yavar Kian (2, 3)

1 CSRC - Beijing Computational Science Research Center [Beijing]
2 CPT - Centre de Physique Théorique - UMR 7332
3 CPT - E8 Dynamique quantique et analyse spectrale

This paper is concerned with inverse source problems for the time-dependent Lamé system and the recovery of initial data 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. 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.

Mots clés: Linear elasticity; stability estimate; time domain; uniqueness; inverse source problems

Domaines: Equations aux dérivées partielles [math.AP]

Guanghui Hu, Yavar Kian. Uniqueness and stability for the recovery of a time-dependent source in elastodynamics. Inverse Problems and Imaging , 2020, 14 (3), pp.463-487. ⟨10.3934/ipi.2020022⟩. ⟨hal-01902820⟩