[1]任丽婷,熊向团*.带有非齐次Dirichlet条件的Helmholtz方程柯西问题的傅里叶方法[J].江西师范大学学报(自然科学版),2019,(02):184-187.[doi:10.16357/j.cnki.issn1000-5862.2019.02.12]
 REN Liting,XIONG Xiangtuan*.The Fourier Method for the Cauchy Problem of the Helmholtz Equation with Inhomogeneous Dirichlet Data[J].Journal of Jiangxi Normal University:Natural Science Edition,2019,(02):184-187.[doi:10.16357/j.cnki.issn1000-5862.2019.02.12]
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带有非齐次Dirichlet条件的Helmholtz方程柯西问题的傅里叶方法()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2019年02期
页码:
184-187
栏目:
数学与应用数学
出版日期:
2019-04-10

文章信息/Info

Title:
The Fourier Method for the Cauchy Problem of the Helmholtz Equation with Inhomogeneous Dirichlet Data
文章编号:
1000-5862(2019)02-0184-04
作者:
任丽婷熊向团*
西北师范大学数学与统计学院,甘肃 兰州 730070
Author(s):
REN LitingXIONG Xiangtuan*
College of Mathematics and Statistics,Northwest Normal University,Lanzhou Gansu 730070,China
关键词:
不适定问题 Helmholtz方程柯西问题 傅里叶方法 Dirichlet条件 误差估计
Keywords:
ill-posed problem Cauchy problem for Helmholtz equation Fourier method Dirichlet data error estimation
分类号:
O 242.2
DOI:
10.16357/j.cnki.issn1000-5862.2019.02.12
文献标志码:
A
摘要:
由于带有非齐次Dirichlet条件的Helmholtz方程柯西问题的解不连续依赖于数据, 所以该问题是严重的不适定问题.利用傅里叶方法给出了该问题在无限条状区域上的正则化近似解,并相应给出了先验与后验的正则化参数选取规则及近似解与精确解的收敛误差估计.
Abstract:
The Cauchy problem for the Helmholtz equation with inhomogeneous Dirichlet data is a severely ill-posed problem,because its solution does not depend continuously on the data.The regularized approximate solution of the problem in an infinite "strip" domain is obtained by a Fourier regularization method.Then,some convergence error estimations with the asymptotic Hölder type error for Fourier regularization method can be proved by using an a priori regularization parameter choice rule and an a posterior regularization parameter choice rule.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2018-10-28 基金项目:国家自然科学基金(11661072)和西北师范大学科学计算创新团队课题(NWNU-LKQN-17-5)资助项目. 通信作者:熊向团(1977-),男,湖北武汉人,副教授,博士,博士生导师,主要从事微分方程数值解研究.e-mail:xiongxt@gmail.com
更新日期/Last Update: 2019-04-10