位置：成果数据库 > 期刊 > 期刊详情页
Laplace方程Cauchy问题的Carasso-Tikhonov正则化方法
  • ISSN号：1005-3085
  • 期刊名称：工程数学学报
  • 时间：0
  • 页码：361-364
  • 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,兰州730000, [2]河南工业大学理学院,郑州450001
  • 相关基金：国家自然科学基金（10671085）;甘肃省自然科学基金（3ZS051-A25-015）;兰州大学理论物理与数学纯基础科学基金（Lzu05-05）.
  • 相关项目：非经典逆热传导问题的正则化理论
作者： 程炜|傅初黎|赵华|
关键词： 不适定问题, Laplace方程的Cauchy问题, 正则化, 误差估计, ill-posed problem, Cauchy problem of Laplace equation, regularization, error estimate
中文摘要：

Laplace方程Cauchy问题是一个众所周知的严重不适定问题。本文给出了二维带状区域中该问题一种新的正则化方法—Carasso-Tikhonov正则化方法,并通过建立一个关键的不等式证明了正则逼近解具有阶数最优的收敛性。

英文摘要：

We give a new Carasso-Tikhonov regularization method for solving the Cauchy problem of Laplace equations, which is a well known and severely ill-posed problem, in the two-dimensional strip region. The order optimal convergence estimate is also provided by introducing a rather technical inequality.

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
同项目期刊论文
On three spectral regularization methods for a backward heat conduction problem
A modified Tikhonov regularization method for a spherically symmetric three-dimensional inverse heat
Fourier regularization for a backward heat equation
Regularization strategies for a two-dimensional inverse heat conduction problem
求解一类反向热传导问题的Fourier正则化和Tikhonov正则化方法
Two approximate methods of a Cauchy problem for the Helmholtz equation
Semi-discrete central difference method for determining surface heat flux of IHCP
A modified method for a backward heat conduction problem
一类求解抛物型方程侧边值问题的最优滤波方法
有界区域上反向热传导问题的La ndweber迭代及算法
An inverseboundaryproblemforone-dimensionalheatequation with amultilayerdomain
Optimal error bound and Fourier regularization for identifying an unknown source in the heat equatio
Two regularization methods for identification of the heat source depending only on spatial variable
Helmholtz 方程 Cauchy 问题的滤波正则化方法
Source term identification for an axisymmetric inverse heat conduction problem
A wavelet-Galerkin method for high order numerical differentiation
A MODIFIED TIKHONOV REGULARIZATION FOR STABLE ANALYTIC CONTINUATION
Identifying an unknown source term in a heat equation
A spectral method for an axisymmetric backward heat equation
Solving the Axisymmetric Inverse Heat Conduction Problem by a Wavelet Dual Least Squares Method
Two regularization methods for an axisymmetric inverse heat conduction problem
Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation
The Fourier regularization for solving the Cauchy problem for the Helmholtz equation
Determining surface heat flux in the steady state for the Cauchy problem for the Laplace equation
The identification of a Robin coefficient by a conjugate gradient method
Reconstruction of the corrosion boundary for the Laplace equation by using a boundary collocation me
Reconstruction of part of a boundary for the Laplace equation by using a regularized method of funda
A meshless method for solving an inverse spacewise-dependent heat source problem
Modified regularization method for the Cauchy problem of the Helmholtz equation
Determining an unknown source in the heat equation by a wavelet dual least squares method
A Bayesian inference approach to identify a Robin coefficient in one-dimensional parabolic problems
关于反向热传导问题的一个条件稳定性结果
A simple regularization method for stable analytic continuation
A spectral regularization method for solving surface heat flux on a general sideways parabolic
Two regularization methods for a Cauchy problem for the Laplace equation
Two regularization methods for a spherically symmetric inverse heat conduction problem
The method of fundamental solutions for the inverse heat source problem
Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded re
Wavelets and regularization of the Cauchy problem for the Laplace equation
一个非标准热方程反向问题的最优滤波正则化方法
浅谈反向热传导问题——“数学物理方程”教学中古典内容与前沿问题相结合的一点探索
Fourier regularization method for solving a Cauchy problem for the Laplace equation
Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation
The method of fundamental solutions for solving a Cauchy problem of Laplace’s equation in a multi-co
修正的Helmholtz方程未知源识别反问题
Poisson方程热源识别反问题
一种求解修正的Helmholtz方程Cauchy问题的数值方法
二维Poisson方程未知源识别反问题
非标准热传导方程的热源识别反问题
含对流项抛物方程的热源识别的拟逆正则化方法
有界区域上含对流项抛物方程的热源识别反问题
非标准抛物方程只含有时间变量的热源识别反问题
抛物方程热源识别的中心差分正则化方法
一类对流-扩散方程热源识别反问题
A Fourth-Order Modified Method for the Cauchy Problem of the Modified Helmholtz Equation
反向热传导问题的一种新的正则化方法
期刊信息
  • 《工程数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:西安交通大学
  • 主编：李大潜
  • 地址：西宁市咸宁西路28号西安交通大学数学与统计学院
  • 邮编：710049
  • 邮箱：jgsx@mail.xjtu.edu.cn
  • 电话：029-82667877
  • 国际标准刊号：ISSN：1005-3085
  • 国内统一刊号：ISSN：61-1269/O1
  • 邮发代号:
  • 获奖情况:
  • 《中文核心期刊要目总览》核心期刊,《中国科学引文数据库》核心期刊,《中国数学文摘》核心期刊,陕西省优秀科技期刊
  • 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,荷兰文摘与引文数据库,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:6741