BEN ABDA, Amel; HENRY, Jacques; JDAY, Fadhel

doi:10.1016/j.crma.2009.03.009

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BEN ABDA, Amel
Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LR-LAMSIN-ENIT]

HENRY, Jacques
Institut de Mathématiques de Bordeaux [IMB]
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]

JDAY, Fadhel
Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LR-LAMSIN-ENIT]

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Comptes rendus de l'Académie des sciences. Série I, Mathématique. 2009, vol. 347, n° 9-10, p. 501-504

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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.< Leer menos

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Missing boundary data reconstruction by the factorization method

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