A mollification method for a Cauchy problem for the Laplace equation

作者：Li, Zhenping^*; Fu, Chuli

来源：Applied Mathematics and Computation, 2011, 217(22): 9209-9218.

DOI：10.1016/j.amc.2011.03.160

• Cauchy problem for Laplace equation
• Ill-posed problem
• Regularization
• Mollification method
• Error estimate

In this paper, we consider a Cauchy problem for the Laplace equation in the strip region 0 < x < 1; y is an element of R, where the Cauchy data is given at x = 0 and the solution is sought in the interval 0 < x <= 1. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. To obtain stable numerical solution, we propose a mollification method (using the Gaussian kernel). Error estimate between the exact solution and its approximation is given. The choices of mollification parameter for a priori and a posteriori are discussed. Numerical examples show that the method works well.

• 出版日期2011-7-15
• 单位洛阳理工学院; 兰州大学