IPI
Recovering conductivity at the boundary in three-dimensional electrical impedance tomography
Gen Nakamura Päivi Ronkanen Samuli Siltanen Kazumi Tanuma
Inverse Problems & Imaging 2011, 5(2): 485-510 doi: 10.3934/ipi.2011.5.485
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.
keywords: localized Dirichlet to Neumann map boundary determination inverse conductivity problem. Electrical impedance tomography
IPI
An inverse boundary value problem for a nonlinear wave equation
Gen Nakamura Michiyuki Watanabe
Inverse Problems & Imaging 2008, 2(1): 121-131 doi: 10.3934/ipi.2008.2.121
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.
keywords: Inverse boundary value problems Nonlinear Wave equations.
IPI
Recovering the boundary corrosion from electrical potential distribution using partial boundary data
Jijun Liu Gen Nakamura
Inverse Problems & Imaging 2017, 11(3): 521-538 doi: 10.3934/ipi.2017024

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.

keywords: Electrical potential Laplace equation boundary impedance uniqueness stability regularization convergence
IPI
The Green function of the interior transmission problem and its applications
Kyoungsun Kim Gen Nakamura Mourad Sini
Inverse Problems & Imaging 2012, 6(3): 487-521 doi: 10.3934/ipi.2012.6.487
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.
keywords: interior transmission problem pseudodifferential operators. Green function
PROC
Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain
Jishan Fan Fucai Li Gen Nakamura
Conference Publications 2015, 2015(special): 387-394 doi: 10.3934/proc.2015.0387
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.
keywords: low Mach number limit. Compressible magnetohydrodynamic equations global existence
DCDS-B
A regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity
Jishan Fan Fucai Li Gen Nakamura
Discrete & Continuous Dynamical Systems - B 2018, 23(4): 1757-1766 doi: 10.3934/dcdsb.2018079

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

keywords: Compressible magnetohydrodynamic equations zero heat conductivity regularity criterion
CPAA
Low Mach number limit of the full compressible Hall-MHD system
Jishan Fan Fucai Li Gen Nakamura
Communications on Pure & Applied Analysis 2017, 16(5): 1731-1740 doi: 10.3934/cpaa.2017084

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.

keywords: Full compressible Hall-MHD system incompressible Hall-MHD system low Mach number limit
CPAA
Global strong solution to the two-dimensional density-dependent magnetohydrodynamic equations with vaccum
Jishan Fan Fucai Li Gen Nakamura
Communications on Pure & Applied Analysis 2014, 13(4): 1481-1490 doi: 10.3934/cpaa.2014.13.1481
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.
keywords: Density-dependent magnetohydrodynamic equations uniform regularity. global existence vaccum

Year of publication

Related Authors

Related Keywords

[Back to Top]