On a three dimensional Cauchy problem for inhomogeneous Helmholtz equation associated with perturbed wave number

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:335

Article

Phong Luu Hong¹  Triet Le Minh^2,3  Quan Pham Hoang⁴ 

[1] Vietnam Natl Univ, Univ Sci, Fac Math, Hanoi, Vietnam

[2] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam

[3] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[4] Sai Gon Univ, Fac Math & Applicat, Ho Chi Minh City, Vietnam

关键词: Cauchy problem;    Helmholtz equation;    Ill-posed problems;    Fourier transform;    Truncation method;    Perturbed wave number;   

DOI  :  10.1016/j.cam.2017.11.042

来源: Elsevier

【 摘 要 】

In recent years, the Cauchy problem for inhomogeneous Helmholtz equation (CPHE) is often considered as the wave number k is a constant number. At present, we investigate a three dimensional CPHE with inhomogeneous Cauchy conditions given at z = 0 while wave number k is perturbed. The problem is well-known to be ill-posed in the sense of Hadamard. Therefore, we regularize the problem by applying the truncation method and possess error estimate between the exact solution and the regularized solution. A numerical experiment is given for the purpose of illustrating our method. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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