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Poisson方程热源识别反问题
  • ISSN号：1003-3998
  • 期刊名称：《数学物理学报：A辑》
  • 时间：0
  • 分类：O175.25[理学—数学;理学—基础数学]
  • 作者机构：[1]兰州理工大学理学院,兰州730050, [2]兰州大学数学与统计学院,兰州730000
  • 相关基金：国家自然科学基金（10671085）和兰州理工大学学校基金（92111,92104）资助
作者： 杨帆[1,2], 傅初黎[2]
关键词： Poisson方程, 热源, 正则化, Carasso-Tikhonov, Poisson equation, Heat source, Regularization, Carasso-Tikhonov.
中文摘要：

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.

英文摘要：

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, H51der 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.

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非经典逆热传导问题的正则化理论
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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:5382