2018
DOI: 10.1002/zamm.201800102
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An iterative regularizing method for an incomplete boundary data problem for the biharmonic equation

Abstract: An incomplete boundary data problem for the biharmonic equation is considered, where the displacement is known throughout the boundary of the solution domain whilst the normal derivative and bending moment are specified on only a portion of the boundary. For this inverse ill‐posed problem an iterative regularizing method is proposed for the stable data reconstruction on the underspecified boundary part. Convergence is proven by showing that the method can be written as a Landweber‐type procedure for an operato… Show more

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Cited by 4 publications
(13 citation statements)
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References 81 publications
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“…We assume that data is given such that there exists a classical or weak solution to (1)- (2). In [10], it is shown that (1)-(2) is ill-posed and that there exists at most one solution. Further in [10], an iterative method is proposed and analysed for the biharmonic data completion.…”
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confidence: 99%
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“…We assume that data is given such that there exists a classical or weak solution to (1)- (2). In [10], it is shown that (1)-(2) is ill-posed and that there exists at most one solution. Further in [10], an iterative method is proposed and analysed for the biharmonic data completion.…”
mentioning
confidence: 99%
“…In [10], it is shown that (1)-(2) is ill-posed and that there exists at most one solution. Further in [10], an iterative method is proposed and analysed for the biharmonic data completion. At each iteration step, mixed boundary value problems are solved for (1) updating functions on the boundary curves.…”
mentioning
confidence: 99%
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