IPI

The aim of electrical impedance tomography (EIT) is to reconstruct the conductivity values inside a conductive object
from electric measurements performed at the boundary of the object. EIT has applications in medical imaging,
nondestructive testing, geological remote sensing and subsurface monitoring. Recovering the conductivity and its
normal derivative at the boundary is a preliminary step in many EIT algorithms; Nakamura and Tanuma introduced
formulae for recovering them approximately from localized voltage-to-current
measurements in [Recent Development in Theories & Numerics, International Conference on Inverse Problems 2003].
The present study extends that work both theoretically and computationally. As a theoretical contribution,
reconstruction formulas are proved in a more general setting. On the computational side, numerical implementation
of the reconstruction formulae is presented in three-dimensional cylindrical geometry.
These experiments, based on simulated noisy EIT data, suggest that the conductivity at the boundary can be recovered
with reasonable accuracy using practically realizable measurements. Further, the normal derivative of the conductivity
can also be recovered in a similar fashion if measurements from a homogeneous conductor (dummy load) are
available for use in a calibration step.

IPI

An inverse boundary value problem for nonlinear wave equation of divergence form in one space dimension is considered. By assuming the nonlinear term is unknown, we show the linear and quadratic part of this term can be identified from the Dirichlet to Neumann map. Here, the nonlinearity is only in terms of the first derivative with respect to the space variable, and the linear and quadratic parts are defined in terms of this derivative. The identification not only gives the uniqueness but also the reconstruction.

IPI

We study detecting a boundary corrosion damage in the inaccessible part of a rectangular shaped electrostatic conductor from a one set of Cauchy data specified on an accessible boundary part of conductor. For this nonlinear ill-posed problem, we prove the uniqueness in a very general framework. Then we establish the conditional stability of Hölder type based on some *a priori* assumptions on the unknown impedance and the electrical current input specified in the accessible part. Finally a regularizing scheme of double regularizing parameters, using the truncation of the series expansion of the solution, is proposed with the convergence analysis on the explicit regularizing solution in terms of a practical average norm for measurement data.

PROC

In this paper we establish the global existence of strong solutions to the
three-dimensional compressible magnetohydrodynamic equations in a bounded domain with small initial
data. Moreover, we study the low Mach number limit to the corresponding problem.

CPAA

In this paper we establish the
global existence of strong solution to the density-dependent incompressible magnetohydrodynamic equations with vaccum in a bounded domain
in $R^2$. Furthermore, the limit as the heat conductivity coefficient tends to zero is also obtained.

IPI

The interior transmission problem appears naturally in the
scattering theory. In this paper, we construct the
Green function associated to this problem. In addition, we provide
point-wise estimates of this Green function similar to those known
for the Green function related to the classical transmission
problems. These estimates are, in particular, useful to the study of
various inverse scattering problems. Here, we apply them to
justify some asymptotic formulas already used for detecting
partially coated dielectric mediums from far field measurements.

CPAA

In this paper we study the low Mach number limit of the full compressible Hall-magnetohydrodynamic (Hall-MHD) system in $\mathbb{T}^3$. We prove that, as the Mach number tends to zero, the strong solution of the full compressible Hall-MHD system converges to that of the incompressible Hall-MHD system.

DCDS-B

We establish a regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity and vacuum in a bounded domain.

KRM

In this paper we establish the uniform estimates of strong solutions with respect to
the Mach number and the dielectric constant to the full compressible Navier-Stokes-Maxwell
system in a bounded domain. Based on these uniform estimates, we obtain
the convergence of the full compressible Navier-Stokes-Maxwell system
to the incompressible magnetohydrodynamic equations for well-prepared data.

DCDS

In this paper we establish some regularity criteria for the three-dimensional
Boussinesq system with the temperature-dependent viscosity and
thermal diffusivity in a bounded domain.