Regularization and New Error Estimates for a Modified Helmholtz Equation

Abstract

We consider the following Cauchy problem for the Helmholtz equation with Dirichlet boundary conditions at x = 0 and x = π    ∆u− ku = 0, (x, y) ∈ (0, π)× (0, 1) u(0, y) = u(π, y) = 0, y ∈ (0, 1) uy(x, 0) = f(x), (x, y) ∈ (0, π)× (0, 1) u(x, 0) = φ(x), 0 < x < π (1) The problem is shown to be ill-posed, as the solution exhibits unstable dependence on… (More)

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Cite this paper

@inproceedings{Tuan2010RegularizationAN, title={Regularization and New Error Estimates for a Modified Helmholtz Equation}, author={Nguyen Huy Tuan and Pham Hoang Quan and Dang Duc Trong and Pham Nguyen Hoang}, year={2010} }