修正的Helmholtz方程未知源识别的Fourier截断正则化方法

Abstract

Abstract:

This paper discusses the problem of determining an unknown source which depends only on one variable for the two dimensional modified Helmholtz equation in a half infinite domain. This problem is ill-posed in the sense that the
solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the Fourier
regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Numerical examples show that our proposed method is effective and stable.

Key words: Modified Helmholtz equation, Unknown source, Regularization, Fourier truncation

CLC Number:

35J05

YANG Fan, FU Chu-Li, LI Xiao-Xiao. The Fourier Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation[J].Acta mathematica scientia,Series A, 2014, 34(4): 1040-1047.

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The Fourier Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation

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