Mathematica Sciences: Inverse Boundary Value Problems

该项目将支持反问题的研究， 偏微分方程 特别是，研究将 聚焦于阻抗断层成像问题， Dirichlet到Neumann映射的特征，逆 各向异性电导率问题 尺寸大于或等于3，以及相关问题 在逆散射和逆问题中， 微分几何 当一个电势被施加到物体的表面时， 导电体，产生的电流通量通过表面 取决于身体的内部阻力。 基于这个理由， 电压和电流测量的边界上， 物体可以用来探测身体的内部结构。 问题是要尽可能多地确定 从电压电位测量的内部电阻率 以及边界处相应的电流通量。 这个问题， 通常被称为阻抗计算机断层摄影或电学 阻抗成像，出现在生物物理学中，试图确定 地球的组成。 最近， 建议作为一个潜在的有价值的诊断工具， 医学和生物科学。

This project will support research on inverse problems in partial differential equations. In particular the research will focus on the impedance tomography problem, the problem of characterization of the Dirichlet to Neumann map, the inverse conductivity problem for anisotropic conductivities in dimensions greater than or equal to three, and related problems in inverse scattering and inverse problems that arise in differential geometry. When an electric potential is applied to the surface of a conducting body, the resulting current flux across the surface depends on the internal resistance of the body. For this reason, voltage and current measurements made on the boundary of an object can be used to probe the internal structure of the body. The problem is to determine as much information as possible about the internal resistivity from measurements of voltage potentials and corresponding current fluxes at the boundary. This problem, often referred to as impedance computed tomography or electrical impedance imaging, arose in geophysics from attempts to determine the composition of the earth. More recently, it has been proposed as a potentially valuable diagnostic tool for the medical and biological sciences.