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2022 Using a Divergence Regularization Method to Solve an Ill-Posed Cauchy Problem for the Helmholtz Equation
Benedict Barnes, Anthony Y. Aidoo, Joseph Ackora-Prah
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Abstr. Appl. Anal. 2022: 1-10 (2022). DOI: 10.1155/2022/4628634

Abstract

The ill-posed Helmholtz equation with inhomogeneous boundary deflection in a Hilbert space is regularized using the divergence regularization method (DRM). The DRM includes a positive integer scaler that homogenizes the inhomogeneous boundary deflection in the Helmholtz equation’s Cauchy issue. This guarantees the existence and uniqueness of the equation’s solution. To reestablish the stability of the regularized Helmholtz equation and regularized Cauchy boundary conditions, the DRM uses its regularization term 1+α2mem, where α>0 is the regularization parameter. As a result, DRM restores all three Hadamard requirements for well-posedness.

Acknowledgments

We acknowledge the contributions of the late E. Osei Frimpong to this research.

Citation

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Benedict Barnes. Anthony Y. Aidoo. Joseph Ackora-Prah. "Using a Divergence Regularization Method to Solve an Ill-Posed Cauchy Problem for the Helmholtz Equation." Abstr. Appl. Anal. 2022 1 - 10, 2022. https://doi.org/10.1155/2022/4628634

Information

Received: 20 September 2021; Accepted: 11 March 2022; Published: 2022
First available in Project Euclid: 28 July 2022

Digital Object Identifier: 10.1155/2022/4628634

Rights: Copyright © 2022 Hindawi

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