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一类求解抛物型方程侧边值问题的最优滤波方法
  • 期刊名称：数学物理学报(中文版)
  • 时间：0
  • 页码：245-252
  • 语言：中文
  • 分类：O175[理学—数学;理学—基础数学]
  • 作者机构：[1]兰州大学数学与统计学院,甘肃兰州730000, [2]中国石油大学（华东）数学与计算科学学院,山东东营257061, [3]复旦大学数学科学学院,上海200433, [4]艺洛软件技术（上海）有限公司,上海201203
  • 相关基金：基金项目：国家自然科学基金（10671085）、兰州大学理论物理与数学纯基础科学基金（Lzu05005）和中国石油大学（华东）引进人才（博士）科研基金（Y080807）资助
  • 相关项目：非经典逆热传导问题的正则化理论
作者： 熊向团|傅初黎|南楠|李洪芳|
关键词： 不适定问题, 抛物型方程侧边值问题, 最优滤波方法, 误差估计., Ill-posed problem, Sideways parabolic equation, Optimal filter method, Error estimate,
中文摘要：

该文考虑一类特殊的抛物型方程侧边值问题，即一类含有对流项的非标准逆热传导问题．给定在x=1处的温度测量值来确定区间（0，1）上的未知解μ（x，t）．这是一类不适定问题，即问题的解（如果解存在）不连续依赖于数据．为了求解这一问题，必须采用某些正则化技巧．该文给出了一种最优滤波方法，使得问题的真实解和近似解之间的误差估计达到了Ho1der型最优．同时还证明了问题的解在x=0处的收敛性．

英文摘要：

The authors consider a sideways parabolic equation in the quarter plane, i.e., a non-standard inverse heat conduction equation with convection term. People want determine the solution μ（x, t） for 0 〈 x 〈 1 from the data along the line x = 1. This is an ill-posed problem in the sense that the solution （if it exists） does not depend continuously on the data. Some special regularization method is needed for solving this problem. This paper considers an optimal filtering method and gives the HSlder optimal error estimate between the exact solution and its regularized approximation solution. Furthermore, the convergence of the regularized approximation solution at x = 0 is also obtained.

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非经典逆热传导问题的正则化理论
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