• Corpus ID: 207847308

About an inverse electromagnetic coefficient problem: uniqueness with partial boundary data and quasi-reversibility method for data completion

@article{Darbas2019AboutAI,
  title={About an inverse electromagnetic coefficient problem: uniqueness with partial boundary data and quasi-reversibility method for data completion},
  author={Marion Darbas and J'er'emy Heleine and Stephanie Lohrengel},
  journal={ArXiv},
  year={2019},
  volume={abs/1911.02806}
}
This paper deals with two questions relative to the inverse coefficient problem of recovering the electric permittivity and conductivity of a medium from partial boundary data at a fixed frequency. The underlying model is the time-harmonic Maxwell equations in the electric field. First, an identifiability result is proved for partial boundary data without restrictive conditions on the inaccessible part of the boundary. The second issue that is addressed, is the data completion problem on the… 
[PDF] Semantic Reader
1 Citations

One Citation

Identification de paramètres électromagnétiques par imagerie micro-ondes

Dans cette these, nous etudions, d'un point de vue theorique et numerique, l'imagerie micro-ondes. Mathematiquement, il s'agit de resoudre un probleme inverse : reconstruire les coefficients…

References

SHOWING 1-10 OF 41 REFERENCES

Uniqueness for an inverse problem in electromagnetism with partial data

A linearized inverse boundary value problem for Maxwell's equations

Inverse problems for time harmonic electrodynamics

We study the inverse boundary value and inverse scattering problems for time-harmonic Maxwell’s equations. The goal is to recover electromagnetic material parameters (permittivity, conductivity and…

Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems

We study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to…

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…

Solving Cauchy problems by minimizing an energy-like functional

An energy-like error functional is introduced in the context of the ill-posed problem of boundary data recovering, which is well known as a Cauchy problem. Links with existing methods for data…

On Cauchy's problem: I. A variational Steklov–Poincaré theory

In 1923 (Lectures on Cauchy's Problem in Linear PDEs (New York, 1953)), J Hadamard considered a particular example to illustrate the ill-posedness of the Cauchy problem for elliptic partial…

On Cauchy's problem: II. Completion, regularization and approximation

In Ben Belgacem and El Fekih (2005 On Cauchy's problem: I. A variational Steklov–Poincaré theory Inverse Problems 21 1915–36), a new variational theory is introduced for the data completion Cauchy…

A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation

This work concerns the use of the method of quasi-reversibility to solve the Cauchy problem for Laplace's equation. We describe a mixed formulation of the method and its relationship with a classical…

A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems

This paper is dedicated to a new way of presenting the Tikhonov regularization in the form of a mixed formulation. Such formulation is well adapted to the regularization of linear ill-posed partial…