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.
Highlights
We recall that the Lamé system (1.1)-(1.2) is frequently used for the study of linear elasticity and imaging problems
More precisely our problem can be connected to mathematical model of the thermoacoustic tomography (TAT) procedure where one wants to recover the absorption of a biological object subjected to a short radiofrequency pulse
Let us first remark that to our best knowledge Theorem 1 is the first result of recovery of source terms stated for the Lamé system outside a cavity
Summary
Where T U is the stress boundary condition defined by (2.2) (see Section 2). In this paper we consider the inverse problem of determining the source term F and the initial conditions V0 and V1 from knowledge of U on the surface ∂BR = {x ∈ R3 : |x| = R} with R > 0 sufficiently large. According to [7, Remark 4.5], even for V0 = V1 = 0, there is an obstruction for the recovery of general time-dependent source terms F. Facing this obstruction we consider this problem for some specific type of source terms
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