Modified auxiliary boundary conditions method for an ill-posed problem for the homogeneous biharmonic equation |
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Authors: | Abderafik Benrabah Nadjib Boussetila Faouzia Rebbani |
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Institution: | 1. Department of Mathematics, FMISM, University 8 Mai 1945 Guelma, Guelma, Algeria;2. Higher School of Industrial Technologies, PO Box 218, Annaba 23000, Algeria |
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Abstract: | In this paper, we are interested in the inverse problem for the biharmonic equation posed on a rectangle, which is of great importance in many areas of industry and engineering. We show that the problem under consideration is ill-posed; therefore, to solve it, we opted for a regularization method via modified auxiliary boundary conditions. The numerical implementation is based on the application of the semidiscrete finite difference method for a sequence of well-posed direct problems depending on a small parameter of regularization. Numerical results are performed for a rectangle domain showing the effectiveness of the proposed method. |
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Keywords: | auxiliary boundary conditions biharmonic equation convergence estimate ill-posed problems plates regularization |
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