Modified nonlocal boundary value problem method for an ill-posed problem for the biharmonic equation

In this paper, we propose a modified nonlocal boundary value problem method for an homogeneous biharmonic equation in a rectangular domain. We show that the considered problem is ill-posed in the sense of Hadamard, i.e. the solution does not depend continuously on the given data. Convergence estimat...

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Bibliographic Details
Published in:Inverse problems in science and engineering Vol. 27; no. 3; pp. 340 - 368
Main Authors: Benrabah, A., Boussetila, N.
Format: Journal Article
Language:English
Published: Taylor & Francis 04.03.2019
Subjects:
a priori estimates
Biharmonic equation
convergence estimate
ill-posed problem
regularization method
ISSN:1741-5977, 1741-5985
Online Access:Get full text
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Summary:In this paper, we propose a modified nonlocal boundary value problem method for an homogeneous biharmonic equation in a rectangular domain. We show that the considered problem is ill-posed in the sense of Hadamard, i.e. the solution does not depend continuously on the given data. Convergence estimates for the regularized solution are obtained under a priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method.
ISSN:1741-5977
1741-5985
DOI:10.1080/17415977.2018.1461859