Poisson方程热源识别反问题

The Inverse Problem of the Identification of the Heat Source for the Poisson Equation

探讨了半带状区域上二维Poisson方程只含有一个空间变量的热源识别反问题.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Carasso-Tikhonov正则化方法,得到了问题的一个正则近似解,并且给出了正则解和精确解之间具有Holder型误差估计.数值实验表明Carasso-Tikhonov正则化方法对于这种热源识别是非常有效的.

This paper discusses the inverse problem of determining a space-wise heat source in the Poisson equation in a half strip domain. This problem is ill-posed, i.e., the solution does not depend continuously on the given data. A regularization solution of the inverse problem is obtained by the Carasso-Tikhonov regularization method. For the regularization solution, H51der type stability estimate is obtained between the regularization solution and the exact solution. A numerical example shows that the Carasso-Tikhonov regularization method works effectively for identification the heat source.