Lipschitz Stability of an Inverse Boundary Value Problem for Time-harmonic Elastic Waves, Part I: Recovery of the Density
نویسندگان
چکیده
We study the inverse boundary value problem for the time-harmonic elastic waves. We focus on the recovery of the density and assume the sti↵ness tensor to be isotropic. The data are the Dirichlet-to-Neumann map. We establish a Lipschitz type stability estimate assuming that the density is piecewise constant with an underlying domain partitioning consisting of a finite number of subdomains.
منابع مشابه
Uniqueness and Lipschitz Stability of an Inverse Boundary Value Problem for Time-harmonic Elastic Waves
where Ω is an open and bounded domain with smooth boundary, ∇̂u denotes the strain tensor, ∇̂u := 12 (∇u + (∇u)T ), ψ ∈ H(∂Ω) is the boundary displacement or source, and C ∈ L(Ω) denotes the isotropic elasticity tensor with Lamé parameters λ, μ: C = λI3 ⊗ I3 + 2μIsym, a.e. in Ω, where I3 is 3 × 3 identity matrix and Isym is the fourth order tensor such that IsymA = Â, ρ ∈ L(Ω) is the density, and...
متن کاملTHE EFFECT OF PURE SHEAR ON THE REFLECTION OF PLANE WAVES AT THE BOUNDARY OF AN ELASTIC HALF-SPACE
This paper is concerned with the effect of pure shear on the reflection from a plane boundary of infinitesimal plane waves propagating in a half-space of incompressible isotropic elastic material. For a special class of constitutive laws it is shown that an incident plane harmonic wave propagating in the considered plane gives rise to a surface wave in addition to a reflected wave (with angle o...
متن کاملDirect and Inverse Elastic Scattering Problems for Diffraction Gratings
This paper is concerned with the direct and inverse scattering of time-harmonic plane elastic waves by unbounded periodic structures (diffraction gratings). We present a variational approach to the forward scattering problems with Lipschitz grating profiles and give a survey of recent uniqueness and existence results. Concerning the inverse problem, global uniqueness results within the class of...
متن کاملSolution of Inverse Euler-Bernoulli Problem with Integral Overdetermination and Periodic Boundary Conditions
In this work, we tried to find the inverse coefficient in the Euler problem with over determination conditions. It showed the existence, stability of the solution by iteration method and linearization method was used for this problem in numerical part. Also two examples are presented with figures.
متن کاملInverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions
In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...
متن کامل