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

DOI10.1016/j.cam.2017.11.042zbMath1390.35109OpenAlexW2773853493MaRDI QIDQ1743921

Luu Hong Phong, Le Minh Triet, Pham Hoang Quan

Publication date: 16 April 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.11.042

zbMATH Keywords

Fourier transformCauchy problemHelmholtz equationill-posed problemstruncation methodperturbed wave number

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Heat equation (35K05) Nonlinear ill-posed problems (47J06) Parabolic equations and parabolic systems (35K99)

Related Items (6)

A kind of operator regularization method for Cauchy problem of the Helmholtz equation in a multi-dimensional case ⋮ A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations ⋮ Analysis of Dirichlet-Robin iterations for solving the Cauchy problem for elliptic equations ⋮ Regularizing a final value problem for nonlinear modified Helmholtz equation with randomly perturbed data ⋮ A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation ⋮ The bi-Helmholtz equation with Cauchy conditions: ill-posedness and regularization methods

Cites Work

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• Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations
• A general filter regularization method to solve the three dimensional Cauchy problem for inhomogeneous Helmholtz-type equations: theory and numerical simulation
• BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method
• An adaptive fast solver for the modified Helmholtz equation in two dimensions
• A Fourth-Order Modified Method for the Cauchy Problem of the Modified Helmholtz Equation

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