ABSTRACT

In this article, we consider an inverse source problem for Poisson equation in a strip domain. That is to determine source term in the Poisson equation from a noisy boundary data. This is an ill-posed problem in the sense of Hadamard, i.e., small changes in the data can cause arbitrarily large changes in the results. Before we give the main results about our proposed problem, we display some useful lemmas at first. Then we propose a modified quasi-reversibility regularization method to deal with the inverse source problem and obtain a convergence rate by using an a priori regularization parameter choice rule. Numerical examples are provided to show the effectiveness of the proposed method.

摘要

在本文中，我们考虑带状域中泊松方程的逆源问题。即从噪声边界数据确定泊松方程中的源项。这是Hadamard意义上的不适定问题，即数据的微小变化可能导致结果的任意大的变化。在我们给出关于我们提出的问题的主要结果之前，我们首先展示一些有用的引理。然后我们提出了一种改进的准可逆正则化方法来处理逆源问题，并通过使用先验正则化参数选择规则来获得收敛速度。数值例子显示了所提出方法的有效性。