Missing boundary data reconstruction by the factorization method

Amel Ben Abda 1 Jacques Henry 2, 3 Fadhel Jday 1
3 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics
Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We consider the data completion problem for the Laplace equation in a cylindrical domain. The Neumann and Dirichlet boundary conditions are given on one face of the cylinder while there is no condition on the other face. This Cauchy problem has been known since Hadamard (1953) to be ill-posed. Here it is set as an optimal control problem with a regularized cost function. We use the factorization method for elliptic boundary value problems. For each set of Cauchy data, to obtain the estimate of the missing data one has to solve a parabolic Cauchy problem in the cylinder and a linear equation. The operator appearing in these problems satisfy a Riccati equation that does not depend on the data.
Type de document :
Article dans une revue
Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2009, 347 (9-10), pp.501-504. 〈10.1016/j.crma.2009.03.009〉
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https://hal.inria.fr/inria-00387688
Contributeur : Jacques Henry <>
Soumis le : lundi 25 mai 2009 - 17:45:37
Dernière modification le : jeudi 11 janvier 2018 - 06:22:11

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Amel Ben Abda, Jacques Henry, Fadhel Jday. Missing boundary data reconstruction by the factorization method. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2009, 347 (9-10), pp.501-504. 〈10.1016/j.crma.2009.03.009〉. 〈inria-00387688〉

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