Poisson方程未知源识别的拟边界正则化方法

Quasi-boundary regularization method for identifying unknown source in Poisson equation

探讨了半带型区域上二维Poisson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)不连续依赖于测量数据.利用拟边界正则化方法,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具有Hler型误差估计.数值实验表明拟边界正则化方法对于这种未知源识别反问题是非常有效的.

The inverse problem of identification of unknown source in two-dimensional Poisson equation with only one space variable in a half-band domain is explored. Such problem is ill-posed in the sense that its solution （if exists） does not depend continuously on the measured data. A regular approximate solution of the problem is obtained with the method of quasi-boundary regularization. Moreover, the Holer-type er- ror estimate between regularization solution and exact solution is given. Numerical experiment shows that the quasi-boundary regularization method will be very effective for such inverse problem of unknown source identification.