Dynamic Boundary Measurements Research Articles

On the identification of the heat conductivity distribution from partial dynamic boundary measurements

ABSTRACT This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary) dynamic boundary measurements and for finite interval in time. By constructing of appropriate test functions, using a control method, we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the diffusion coefficient as the leading order of an appropriate averaging of the partial dynamic boundary measurements.

Reconstruction of polygonal inclusions in a heat conductive body from dynamical boundary data

In this paper, we consider a reconstruction problem of small and polygonal heat-conducting inhomogeneities from dynamic boundary measurements on part of the boundary and for finite interval in time. Our identification procedure is based on asymptotic method combined with appropriate averaging of the partial dynamic boundary measurements. Our approach is expected to lead to an effective computational identification algorithms.

On an inverse boundary problem for the heat equation when small heat conductivity defects are present in a material

For the heat equation in a bounded domain we consider the inverse problem of identifying locations and certain properties of the shapes of small heat‐conducting inhomogeneities from dynamic boundary measurements on part of the boundary and for finite interval in time. The key ingredient is an asymptotic method based on appropriate averaging of the partial dynamic boundary measurements. Our approach is expected to lead to very effective computational identification algorithms.

Numerical Reconstruction of Small Perturbations in the Electromagnetic Coefficients of a Dielectric Material

The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measurements. Our numerical algorithm is based on the resolution of the time-dependent Maxwell equations, an exact controllability method and Fourier inversion for localizing the perturbations. Two-dimensional numerical experiments illustrate the performance of the reconstruction method for dierent congurations even

On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements

This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation in a bounded smooth domain in ℝd from partial (on part of the boundary) dynamic boundary measurements. In this paper, we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the coefficient c provided that c is known outside a bounded domain. Then, through construction of appropriate test functions by a geometrical control method, we derive a formula for calculating the coefficient c from the knowledge of the difference between the local Dirichlet‐to‐Neumann maps.

An inverse problem for a linear Schrödinger equation in the presence of inhomogeneities of small volumes

AbstractIn this paper we prove that the knowledge of the partial (on part of the boundary) dynamic boundary measurements for the Schrödinger equation on any open subset Γ of the boundary determines uniquely the potential. Using a global Carleman estimate, we also derive a stability result with appropriate norms provided that Γ satisfies a suitable geometrical condition.

Reconstruction of closely spaced small inhomogeneities via boundary measurements for the full time-dependent Maxwell’s equations

We consider for the full time-dependent Maxwell’s equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements on the boundary for a finite time interval.

Determination of small amplitude perturbations for the electric permittivity from partial dynamic boundary measurements

The paper deals with reconstruction of small perturbation of the uniform isotropic complex electric permittivity from dynamic measurements of the tangential component of the magnetic field on the boundary (or a part of the boundary) of a domain. The method is based on derived asymptotic inverse Fourier transform of the perturbation in the complex permittivity. Through construction of appropriate test functions by a geometrical control method, we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the electric permittivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations.

Reconstruction of Elastic Inclusions of Small Volume via Dynamic Measurements

We consider the inverse problem of identifying locations and certain properties of the shapes of small elastic inclusions in a homogeneous background medium from dynamic boundary measurements for a finite interval in time. Using particular background solutions as weights, we present an asymptotic method based on appropriate averaging of the dynamic boundary measurements and propose non-iterative algorithms for solving our inverse problem.

Identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements

We consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial (on part of the boundary) dynamic boundary measurements. Through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations. This asymptotic formula is generalized to the full time-dependent Maxwell's equations. Our formulae may be expected to lead to very effective computational identification algorithms, aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements.

An Inverse Initial Boundary Value Problem for the Wave Equation in the Presence of Imperfections of Small Volume

We consider for the wave equation the inverse problem of identifying locations and certain properties of the shapes of small conductivity inhomogeneities in a homogeneous background medium from dynamic boundary measurements on part of the boundary and for a finite interval in time. Using as weights particular background solutions constructed by a geometrical control method, we develop an asymptotic method based on appropriate averaging of the partial dynamic boundary measurements. Our approach is expected to lead to very effective computational identification algorithms.

Recovery of small electromagnetic inhomogeneities from partial boundary measurements

We consider for the inverse problem of identifying locations and certain properties of the shapes of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on part of the boundary or dynamic boundary measurements for a finite time interval. Using as weights particular background solutions we develop asymptotic methods based on appropriate averaging of the data. To cite this article: H. Ammari, A.G. Ramm, C. R. Mecanique 330 (2002) 199–205.