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| HAL: inria-00617511, version 1 |
| DOI: 10.1088/0266-5611/27/5/055014 |
| See detailed view |  BibTeX,EndNote,... |
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| Inverse Problems 27, 5 (2011) |
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| Boundary data completion: the method of boundary value problem factorization |
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| Amel Ben Abda 1Jacques Henry 2, 3 |
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| (2011-04-18) |
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| We consider the following data completion problem for the Laplace equation in the cylindrical domain: = ]0, a[×O,O ⊂ Rn−1 (O is a smooth bounded open set anda > 0), limited by the faces 0 = {0}×O and a = {a}×O. The Neumann and Dirichlet boundary conditions are given on 0 while no condition is given on a. The completion data problem consists in recovering a boundary condition on a. This problem has been known to be ill-posed since Hadamard [12]. The problem is set as an optimal control problem with a regularized cost function. To obtain directly an approximation of the missing data on a we use the method of factorization of elliptic boundary value problems. This method allows us to factorize a boundary value problem in the product of two parabolic problems. Here it is applied to the optimality system (i.e. jointly on the state and adjoint state equations). |
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| 1: | Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur (LAMSIN) |
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ENIT |
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| 2: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 3: | ANUBIS (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR |
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| Domain | : | Mathematics/Analysis of PDEs |
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| inria-00617511, version 1 | |
| http://hal.inria.fr/inria-00617511 | |
| oai:hal.inria.fr:inria-00617511 | |
| From: Jacques Henry | |
| Submitted on: Monday, 29 August 2011 13:11:00 | |
| Updated on: Monday, 29 August 2011 14:11:53 | |
