Uniqueness and Stability of Determining the Residual Stress by One Measurement

Lipschitz stability in determining density and two Lamé coefficients

“…As for similar inverse problems for the Lamé system with residual stress, see Isakov, Wang and Yamamoto [31], Lin and Wang [44].…”

Global uniqueness and Lipschitz stability of residual stress from one boundary measurement

“…We give explicit pseudo-convexity conditions for ψ(x, t) = |x − β| 2 − θ 2 t 2 in the most general case. Also we show that explicit smallness condition on R (compared to nonexplicit conditions in [8], [9]) suffices for pseudo-convexity. Smallness of residual stress is a natural assumption for applications to geophysics and material science.…”

“…Then our conditions on the coefficients of residual stress systems and on G by known energy estimates (like in [3], [9]) imply that…”

“…We are interested in recovery of the residual stress from additional boundary data. This system is anisotropic, which creates a challenge for its identification: there are only recent results [9], [10] when R is small. The goal of this paper is to obtain uniqueness and the (best possible) Lipschitz stability results without any smallness assumption.…”

Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress

“…In particular, they were a main tool in the first proof of uniqueness and stability of all three elastic parameters in the dynamical Lamé system from two sets of boundary data [6]. Anisotropic systems have been studied only in some (important) particular cases, like small scalar perturbation of classical elasticity (elasticity with residual stress) in [11], [12], [13] where there are Carleman estimates, unique continuation and stability of identification of elastic coefficients for such systems.…”