|
| 摘要: |
| 本文研究了一类不适定的非线性椭圆方程柯西问题.利用一种正则化方法克服其不适定性，获得了正则化解的存在唯一性，稳定性及收敛性结果，并构造一种迭代格式计算了正则化解，推广了已有文献在椭圆方程柯西问题正则化理论与算法方面的相关研究结果. |
| 关键词: 不适定问题 柯西问题 非线性椭圆方程 正则化方法 |
| DOI： |
| 分类号:O175.25;O175.29 |
| 基金项目:Supported by the Science Research Project of Ningxia Higher School (NGY2017169). |
|
| REGULARIZATION METHOD FOR AN ILL-POSED CAUCHY PROBLEM OF NONLINEAR ELLIPTIC EQUATION |
|
ZHANG Hong-wu,ZHANG Xiao-ju
|
| Abstract: |
| This paper considers an ill-posed Cauchy problem of nonlinear elliptic equation. By using a regularization method to overcome the ill-posedness, we obtain the existence, uniqueness, stability and convergence result of the regularization solution, and an iterative scheme is constructed to calculate the regularization solution, which is an extension on the related research results of existing literature in the aspect of regularization theory and algorithm for Cauchy problem of elliptic equation. |
| Key words: ill-posed problem Cauchy problem nonlinear elliptic equation regularization method |
