# On a Bernoulli problem with geometric constraints

Abstract : A Bernoulli free boundary problem with geometrical constraints is studied. The domain $\Om$ is constrained to lie in the half space determined by $x_1\geq 0$ and its boundary to contain a segment of the hyperplane $\{x_1=0\}$ where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic properties of the solution and then to the numerical treatment of the problem using a shape optimization formulation. The major difficulty and originality of this paper lies in the treatment of the geometric constraints.
Keywords :
Type de document :
Article dans une revue

Littérature citée [27 références]

https://hal.archives-ouvertes.fr/hal-00462494
Contributeur : Yannick Privat <>
Soumis le : mercredi 13 octobre 2010 - 19:00:01
Dernière modification le : vendredi 16 novembre 2018 - 01:22:44
Archivage à long terme le : vendredi 14 janvier 2011 - 03:14:08

### Fichiers

bernLP_Hal.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Antoine Laurain, Yannick Privat. On a Bernoulli problem with geometric constraints. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2012, 18 (1), pp.157-180. ⟨10.1051/cocv/2010049⟩. ⟨hal-00462494v2⟩

### Métriques

Consultations de la notice

## 348

Téléchargements de fichiers