数学杂志2020，Vol.40Issue(5)：519-538,20.
Helmholtz型方程柯西问题的修正Lavrentiev正则化方法
MODIFIED LAVRENTIEV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF HELMHOLTZ-TYPE EQUATION
摘要
Abstract
In this paper, a Cauchy problem of Helmholtz-type equation with nonhomogeneous Dirichlet and Neumann datum is researched. We establish the result of conditional stability under an a-priori assumption for exact solution. A modified Lavrentiev regularization method is used to overcome its ill-posedness, and under an a-priori and an a-posteriori selection rule for the regular-ization parameter we obtain the convergence result for the regularized solution, the corresponding results of numerical experiments verify that the proposed method is stable and workable,this work is an extension on the related research results of existing literature in the aspect of regularization theory and algorithm for Cauchy problem of Helmholtz-type equation.关键词
不适定问题/柯西问题/Helmholtz型方程/修正Lavrentiev正则化方法/收敛性估计Key words
ill-posed problem/Cauchy problem/Helmholtz-type equation/modified Lavren-tiev method/convergence estimate分类
数理科学引用本文复制引用
张宏武,张晓菊..Helmholtz型方程柯西问题的修正Lavrentiev正则化方法[J].数学杂志,2020,40(5):519-538,20.基金项目
Supported by the NSF of China(11761004) （11761004）
NSF of Ningxia(2019AAC03128). （2019AAC03128）
