摘要：In this paper, we consider a Cauchy problem for the Poisson equation with nonhomogeneous source. The problem is shown to be ill-posed as the solution exhibits unstable dependence on the given data function. Using a new method, we regularize the given problem and obtain some new results. Two numerical examples are given to illustrate the effectiveness of our method. MSC:35K05, 35K99, 47J06, 47H10.
关键词：Poisson equation ; Cauchy problem ; ill-posed problem ; convergence estimates
