Some remarks on a modified Helmholtz equation with inhomogeneous source

DOI10.1016/J.APM.2012.03.014zbMath1352.65442OpenAlexW2060506252MaRDI QIDQ350378

Quoc Viet Tran, Van Thinh Nguyen, Nguyen Huy Tuan

Publication date: 7 December 2016

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2012.03.014

zbMATH Keywords

Cauchy problemill-posed problemHelmholtzhomogeneous and inhomogeneous source

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (10)

Landweber iterative regularization method for identifying the unknown source of the modified Helmholtz equation ⋮ Reconstruction of the electric field of the Helmholtz equation in three dimensions ⋮ Analysis and numerical simulation of the three-dimensional Cauchy problem for quasi-linear elliptic equations ⋮ Regularization method for an ill-posed Cauchy problem for elliptic equations ⋮ A modified integral equation method of the nonlinear elliptic equation with globally and locally Lipschitz source ⋮ A quasi-boundary value regularization method for determining the heat source ⋮ Landweber iterative regularization method for reconstructing the unknown source of the modified Helmholtz equation ⋮ A new general filter regularization method for Cauchy problems for elliptic equations with a locally Lipschitz nonlinear source ⋮ Adaptive Runge-Kutta regularization for a Cauchy problem of a modified Helmholtz equation ⋮ Regularization of an initial inverse problem for a biharmonic equation

Cites Work

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• Fourth-order modified method for the Cauchy problem for the Laplace equation
• Conditional Stability Estimates and Regularization with Applications to Cauchy Problems for the Helmholtz Equation
• Stability results for the Cauchy problem for the Laplace equation in a strip
• L2-Conditional stability estimate for the Cauchy problem for the Laplace equation
• Algorithm 814

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