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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Vydáno v:Mathematical methods in the applied sciences Ročník 43; číslo 1; s. 358 - 383
Hlavní autoři: Benrabah, Abderafik, Boussetila, Nadjib, Rebbani, Faouzia
Médium: Journal Article
Jazyk:angličtina
Vydáno: Freiburg Wiley Subscription Services, Inc 15.01.2020
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5888