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IPI

In this paper, a time domain enclosure method for an inverse
obstacle scattering problem of electromagnetic wave is introduced.
The wave as a solution of Maxwell's equations is generated by an applied volumetric current having an

*orientation*and supported outside an unknown obstacle and observed on the same support over a finite time interval. It is assumed that the obstacle is a perfect conductor. Two types of analytical formulae which employ a*single*observed wave and explicitly contain information about the geometry of the obstacle are given. In particular, an effect of the orientation of the current is catched in one of two formulae. Two corollaries concerning with the detection of the points on the surface of the obstacle nearest to the centre of the current support and curvatures at the points are also given.
IPI

An inverse obstacle scattering problem for the wave governed by the Maxwell system in the time domain, in particular, over a finite time interval is considered. It is assumed that the electric field $\boldsymbol{E}$ and magnetic field $\boldsymbol{ H}$ which are solutions of the Maxwell system are generated only by a current density at the initial time located not far a way from an unknown obstacle. The obstacle is embedded in a medium like air which has constant electric permittivity $ε$ and magnetic permeability $μ$. It is assumed that the fields on the surface of the obstacle satisfy the Leontovich boundary condition $\boldsymbol{ ν}×\boldsymbol{H}-λ\,\boldsymbol{ ν}×(\boldsymbol{ E}×\boldsymbol{ ν})=\boldsymbol{ 0}$ with admittance $λ$ an unknown positive function and $\boldsymbol{ ν}$ the unit outward normal. The observation data are given by the electric field observed at the same place as the support of the current density over a finite time interval. It is shown that an indicator function computed from the electric fields corresponding two current densities enables us to know: the distance of the center of the common spherical support of the current densities to the obstacle; whether the value of the admittance $λ$ is greater or less than the special value $\sqrt{ε/μ}$.

IPI

An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method

This paper studies a prototype of inverse initial boundary value
problems whose governing equation is the heat equation in three
dimensions. An unknown discontinuity embedded in a three-dimensional
heat conductive body is considered.
A

*single*set of the temperature and heat flux on the lateral boundary for a fixed observation time is given as an observation datum. It is shown that this datum yields the minimum length of broken paths that start at a given point outside the body, go to a point on the boundary of the unknown discontinuity and return to a point on the boundary of the body under some conditions on the input heat flux, the unknown discontinuity and the body. This is new information obtained by using enclosure method.
keywords:
corrosion
,
thermal imaging
,
cavity
,
heat equation
,
enclosure method.
,
Inverse boundary value problem

IPI

Inverse obstacle scattering aims to extract information about distant and unknown targets using wave propagation. This study concentrates on a two-dimensional setting using time-harmonic acoustic plane waves as incident fields and taking the obstacles to be sound-hard with smooth or polygonal boundary. Measurement data is simulated by sending one incident wave towards the area of interest and computing the far field pattern (1) on the whole circle of observation directions, (2) only in directions close to backscattering, and (3) only in directions close to forward-scattering. A variant of the enclosure method is introduced, based on applying the far field operator to an explicitly constructed density, yielding information about the convex hull of the obstacle. The numerical evidence presented suggests that the convex hull of obstacles can be approximately recovered from noisy limited-aperture far field data.

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