修正的Helmholtz方程未知源识别反问题

The Inverse Problem of Identifying the Unknown Source for the Modified Helmholtz Equation

探讨半带状区域上二维修正的Helmholtz方程只含有一个空间变量的未知源识别反问题.这类问题是不适定的,即问题的解(如果存在的话)不连续依赖于测量数据.利用拟可逆正则化方法,得到问题的一个正则近似解,并且给出正则解和精确解之间收敛的误差估计.数值实验表明拟可逆正则化方法对于这种未知源识别非常有效.

This paper discusses the inverse problem of determining a spacewise unknonwn source for the two dimensional modified Helmholtz equation in a half strip domain. This problem is ill-posed, i.e., the solution does not depend continuously on the data. A regularization solution of the inverse problem is obtained by the quasi-reversibility regularization method. For the regularization solution, convergence estimate is obtained between the regularization solution and the exact solution. The numerical example shows that the quasi-reversibility regularization method works effectively for identification of the unknown source.