Conditional stability estimate for an ill-posed elliptic equation by using nonlocal conditions

• Autorzy: Benrabah Abderafik

Identyfikatory

DOI

10.17512/jamcm.2022.3.01

• Języki publikacji: EN

Abstrakty

EN

We consider an ill-posed linear homogeneous fourth-order elliptic equation. We show that the problem is ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the given data. We propose a regularization method via nonlocal conditions and under some a priori bound assumptions different estimates for the regularized solution are obtained. Numerical examples for a rectangle domain show the effectiveness of the new method in providing highly accurate numerical solutions as the noise level tends to zero.

Słowa kluczowe

EN

ill-posed problem; biharmonic equation; regularization methods; nonlocal conditions; a priori estimates

PL

problem źle postawiony; równanie biharmoniczne; metoda regularyzacji; warunki nielokalne; szacowanie a priori

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2022
• Tom: Vol. 21, nr 3
• Strony: 5--17
• Opis fizyczny: Bibliogr. 21 poz., rys., tab.

Twórcy

autor

Benrabah Abderafik

• Department of Mathematics, University 8 Mai, 1945 Guelma, Algeria

Bibliografia

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• [17] Benrabah, A., Boussetila, N., & Rebbani, F. (2020). Modified auxiliary boundary conditions method for an illposed problem for the homogeneous biharmonic equation. Math. Methods Appl. Sci., 43, 358-383.
• [18] Merker, J., & Matas, A. (2022). Estimation of discontinuous parameters in linear elliptic equations by a regularized inverse problem. PADIFF, 5, 100384, DOI: 10.1016/j.padiff.2022.100384.
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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).