Reconstructing the right-hand side of a Poisson equation with random noise

descriptionPublicationkeyboard_double_arrow_right Article 28 Mar 2025Publisher:Applied Science & Technology PublishingJournal:Letters on Applied and Pure Mathematics, volume 1, pages 1-7 (eissn: 2980-1982,

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Authors: Gurefe, Yusuf; Long, Le Dinh;

doi: 10.66147/lapm.2023117 , 10.5281/zenodo.7912085 , 10.5281/zenodo.7912084

Reconstructing the right-hand side of a Poisson equation with random noise

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Abstract

An inverse source problem for the Poisson equation is looked at in this article. This is a problem that is poorly posed because even minor changes in the data can result in arbitrarily large changes in the results. We first demonstrate some useful lemmas about our proposed problem before presenting the main results. Then, at that point, we propose a regularization strategy to manage the reverse source issue and get a union rate with random noise.

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Keywords

Conformable derivative, Sobolev embeddings, Inverse source problem, Fourier truncation method

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