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二维Poisson方程未知源识别反问题
  • ISSN号：1673-5196
  • 期刊名称：《兰州理工大学学报》
  • 时间：0
  • 分类：O175.26[理学—数学;理学—基础数学]
  • 作者机构：[1]兰州理工大学理学院,甘肃兰州730050, [2]天津城市建设学院基础学科部,天津300384
  • 相关基金：国家自然科学基金（10671085）.致谢：本文得到兰州理工大学校基金（92111,92104）的资助,在此表示感谢.
作者： 杨帆[1], 万诗敏[2], 李敦刚[1]
关键词： Poisson方程, 未知源, 正则化, 简化的Tikhonov方法, 不适定问题, Poisson equation, unknown , urce, regularization, Simplified Tikhonov method, Ill-posed problem
中文摘要：

探讨二维Poisson方程只含有一个空间变量的未知源识别反问题．这类问题是不适定的，即问题的解不连续依赖于测量数据．利用简化的Tikhonov正则化方法，得到问题的一个正则近似解，并且给出正则解和精确解之间具有Holder型误差估计．

英文摘要：

The inverse problem of identification of unknown source with only one spatial variable was discussed for two-dimensional Poisson equation. This problem was ill-posed, i. e. , the solution does not depend continuously on the data measured. A regularized approximate solution of the inverse problem was obtained by using simplified Tikhonov regularization method. For the regularization solution, Holder-type error estimate was gained between the regularized solution and the exact solution.

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期刊信息
  • 《兰州理工大学学报》
  • 北大核心期刊（2011版）
  • 主管单位:甘肃省教委
  • 主办单位:兰州理工大学
  • 主编：李有堂
  • 地址：甘肃省兰州市兰工坪路287号
  • 邮编：730050
  • 邮箱：journal@lut.cn
  • 电话：0931-2756301
  • 国际标准刊号：ISSN：1673-5196
  • 国内统一刊号：ISSN：62-1081/T
  • 邮发代号:54-72
  • 获奖情况:
  • 甘肃高等校优秀学术期刊,全国优秀高校自然科学学报及教育部优秀科技期刊评...,第二届国家期刊奖百种重点期刊
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  • 被引量:6651