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inria-00617511, version 1

Boundary data completion: the method of boundary value problem factorization

Amel Ben Abda () a, 1, Jacques Henry () 2, 3, Fadhel Jday () b, 1

Inverse Problems 27, 5 (2011)

Résumé : 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).

  • a –  Ecole Nationale dÍngénieurs de Tunis
  • b –  ENIT tunis
  • 1 :  Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur (LAMSIN)
  • ENIT
  • 2 :  Institut de Mathématiques de Bordeaux (IMB)
  • CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
  • 3 :  ANUBIS (INRIA Bordeaux - Sud-Ouest)
  • INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR
  • Domaine : Mathématiques/Equations aux dérivées partielles
 
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  • Contributeur : Jacques Henry <>
  • Soumis le : Lundi 29 Août 2011, 13:11:00
  • Dernière modification le : Lundi 29 Août 2011, 14:11:53