Modified auxiliary boundary conditions method for an ill‐posed problem for the homogeneous biharmonic equation

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 vi...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 43; no. 1; pp. 358 - 383
Main Authors: Benrabah, Abderafik, Boussetila, Nadjib, Rebbani, Faouzia
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 15.01.2020
Subjects:
auxiliary boundary conditions
biharmonic equation
Biharmonic equations
Boundary conditions
convergence estimate
Finite difference method
ill‐posed problems
Inverse problems
plates
Regularization
Regularization methods
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary: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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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5888