|
|||||
|
|
| Poisson方程热源识别反问题 | |
| 引用本文： | 杨帆,傅初黎. Poisson方程热源识别反问题[J]. 数学物理学报(A辑), 2010, 30(4): 1080-1087 |
| 作者姓名： | 杨帆 傅初黎 |
| 作者单位： | 杨帆(兰州理工大学理学院,兰州,730050;兰州大学数学与统计学院,兰州,730000);傅初黎(兰州大学数学与统计学院,兰州,730000) |
| 基金项目： | 国家自然科学基金，兰州理工大学学校基金 |
| 摘 要： | 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. |
| 关 键 词： | Poisson 方程 热源 正则化 Carasso-Tikhonov |
| 收稿时间： | 2008-12-03 |
| 修稿时间： | 2009-10-14 |
he Inverse Problem of the Identification of the Heat Source for the Poisson Equation |
|
| YANG Fan,FU Chu-Li. he Inverse Problem of the Identification of the Heat Source for the Poisson Equation[J]. Acta Mathematica Scientia, 2010, 30(4): 1080-1087 | |
| Authors: | YANG Fan FU Chu-Li |
| Affiliation: | 1.School of Science, Lanzhou University of Technology, Lanzhou 730050;2.School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 |
| Abstract: | 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, Hölder 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. |
| Keywords: | Carasso-Tikhonov |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |
| 点击此处可从《数学物理学报(A辑)》浏览原始摘要信息 | |
| 点击此处可从《数学物理学报(A辑)》下载免费的PDF全文 | |