论文标题
使用实验数据的一维方程的反问题的凸化化
Convexification for an Inverse Problem for a 1D Wave Equation with Experimental Data
论文作者
论文摘要
这里的前进问题是凯奇（Cauchy）的问题是1D双曲线PDE，其主要部分在运算符的主要部分中具有可变系数。该系数是空间分布的介电常数。反问题包括从反向散射边界测量中恢复该介电常数。数据取决于一个变量，即时间。为了解决这个问题，分析了一种新版本的凸化方法。该理论保证了该方法的全球融合。对于计算模拟和实验数据进行了数值测试。实验数据是在现场收集的，模仿了反某人地雷的空间分布的介电常数和简易爆炸装置的问题。
The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the recovery of that dielectric constant from backscattering boundary measurements. The data depend on one variable, which is time. To address this problem, a new version of the convexification method is analytically developed. The theory guarantees the global convergence of this method. Numerical testing is conducted for both computationally simulated and experimental data. Experimental data, which are collected in the field, mimic the problem of the recovery of the spatially distributed dielectric constants of antipersonnel land mines and improvised explosive devices.
