Reconstruction of inclusion from boundary measurements

@inproceedings{Ikehata2002ReconstructionOI,
  title={Reconstruction of inclusion from boundary measurements},
  author={Masaru Ikehata},
  year={2002}
}
Abstract - We consider the problem of reconstructing of the boundary of an unknown inclusion together with its conducticity from the localized Dirichlet-to- Neumann map. We give an exact reconstruction proceduer and apply the method to an inverse boundary value problem for the system of the equations in the theory of elasticity. 
Reconstruction of the support function for inclusion from boundary measurements
Abstract - First we give a formula (procedure) for the reconstruction of the support function for unknown inclusion by means of the Dirichlet to Neumann map. In the procedure we never make use of the
Reconstruction of inclusions for the inverse boundary value problem with mixed type boundary condition
We consider an inverse boundary value problem for identifying the inclusion inside a known anisotropic conductive medium. We give a reconstruction procedure for identifying the inclusion from the
Reconstruction of Inclusions for the Inverse Boundary Value Problem of Non-stationary Heat Equation
An inverse problem for identifying an inclusion inside an isotropic, homogeneous heat conductive medium is considered. The shape of inclusion can change time dependently. For the one space
Reconstruction of Inclusions for the Inverse Boundary Value Problem with Mixed Type Boundary Condition and Source Term
We considered identifying the shape of an unknown inclusion inside an anisotropic conductive medium. The assumption for the regularity of the background conductivity is that which guarantees the weak
Reconstruction of inclusions in an elastic body
We consider the reconstruction of elastic inclusions embedded inside of a planar region, bounded or unbounded, with isotropic inhomogeneous elastic parameters by measuring displacements and tractions
Reconstruction Formula for Identifying Cracks
We consider an inverse boundary value problem for identifying cracks in a conductive medium. By combining the probe method and an analysis for the behavior of the “reflected solution”, we derive a
Reconstruction of cracks in an inhomogeneous anisotropic medium using point sources
TLDR
This work considers the inverse problem, in two and three dimensions, of identifying elastic cracks embedded in an inhomogeneous anisotropic elastic medium using point sources and gives a reconstruction algorithm for this inverse problem.
Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain
We consider the inverse boundary value problem of recovering piecewise homogeneous elastic tensor and piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or
A probe method for the inverse boundary value problem of non-stationary heat equations
An inverse problem for identifying an inclusion inside an isotropic homogeneous heat conductive medium is considered. The shape of the inclusion may vary depending on time. For the one space
Stable Determination of an Inclusion in an Elastic Body by Boundary Measurements
TLDR
This work considers the inverse problem of identifying an unknown inclusion contained in an elastic body by the Dirichlet-to-Neumann map and establishes a logarithmic stability estimate.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 19 REFERENCES
RECONSTRUCTION OF THE SHAPE OF THE INCLUSION BY BOUNDARY MEASUREMENTS
We give a formula for the reconstruction of the shape of the unknown inclusion by means of the Dirichlet to Neumann map.
Global uniqueness for an inverse boundary problem arising in elasticity
SummaryWe prove that we can determine the Lamé parameters of an elastic, isotropic, inhomogeneous medium in dimensionsn≧3, by making measurements of the displacements and corresponding stresses at
Global uniqueness for a two-dimensional inverse boundary value problem
We show that the coefficient -y(x) of the elliptic equation Vie (QyVu) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary, and give a
Singular solutions of elliptic equations and the determination of conductivity by boundary measurements
Abstract We improve some results on uniqueness and stability in the determination of the coefficient a in the equation (i) div( a grad u ) = 0 in Ω, when all possible pairs of Dirichlet and Neumann
A global uniqueness theorem for an inverse boundary value problem
In this paper, we show that the single smooth coefficient of the elliptic operator LY = v yv can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixed
Determining conductivity by boundary measurements II. Interior results
Abstract : In a recent paper the authors showed that an unknown real-analytic conductivity gamma may be determined from static boundary measurements. In this document they extend this analysis by
Unique continuation for a stationary isotropic lamé system with variable coefficients
We give a simple proof of the unique continuation properties for a stationary isotropic Lame system with variable coefficients. The key is that by introducing the divergence component of the
On uniqueness of recovery of a discontinuous conductivity coefficient
On considere le probleme de retrouver le coefficient a de l'equation elliptique div(a⊇u)=0 dans un domaine Ω avec la condition aux limites u=φ sur ∂Ω quand ∂u/∂N est donnee pour tout φ (regulier). On
Identification of the shape of the inclusion having essentially bounded conductivity
Consider an isotropic conductor of electric current which occupies a domain Ω C R(n > 2) with conductivity coefficient 7 = 1 + /ιχζ>, where D is an open subset of Ω with Lipschitz boundary. We assume
Size estimation of inclusion
This paper concerns the estimation of the size(Lebesgue measure) of an unknown inclusion imbedded in a known reference conductor or elasctic body. First, we point out two improvements of the
...
1
2
...