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反向热传导问题的一种新的正则化方法
  • ISSN号：1000-0984
  • 期刊名称：《数学的实践与认识》
  • 时间：0
  • 分类：O551.3[理学—热学与物质分子运动论;理学—物理]
  • 作者机构：[1]河南工业大学理学院,河南郑州450001, [2]兰州大学数学与统计学院,甘肃兰州730000
  • 相关基金：国家自然科学基金（10671085）; 河南省自然科学基金（102300410118）; 河南省教育厅自然科学基金（2009B110007）; 河南工业大学博士基金（2007BS028）
作者： 程炜[1], 侯长顺[1], 傅初黎[2]
关键词： 不适定问题, 反向热传导问题, 正则化, 误差估计, Ill-posed problem, backward heat conduction problem, regularization, error estimation
中文摘要：

讨论一个高维反向热传导问题,这是一个经典的严重不适定问题.关于这一问题我们给出一种新的正则化方法-改进的Tikhonov正则化方法,以恢复解对数据的连续依赖性.通过构造一个重要的不等式和提高先验光滑条件,获得正则解在0〈t〈T时很强的收敛性估计和初始时刻t=0的对数型收敛性估计.

英文摘要：

This paper deals with a backward heat conduction problem in n-dimensional region,it is a classical severely ill-posed problem.we propose a new regularization method-modified Tikhonov regularization method for this problem to recover the stability of solution. Moreover,by introducing a rather technical inequality and improving a-priori smoothness assumption we obtain a quite sharp error estimate between the approximate solution and exact solution in interval 0tT and a logarithmic type convergence estimate at initial time t = 0.

同期刊论文项目
非经典逆热传导问题的正则化理论
期刊论文 60
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期刊信息
  • 《数学的实践与认识》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国科学院数学与系统科学研究院
  • 主编：林群
  • 地址：北京大学数学科学学院
  • 邮编：100871
  • 邮箱：bjmath@math.pku.edu.cn
  • 电话：010-62759981
  • 国际标准刊号：ISSN：1000-0984
  • 国内统一刊号：ISSN：11-2018/O1
  • 邮发代号:2-809
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,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:22973