HAL: hal-00462494, version 2

arXiv: 1010.3144

DOI: 10.1051/cocv/2010049

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ESAIM - Control Optimisation and Calculus of Variations 18, 1 (2012) 157-180

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v1 (2010-03-25)

v2 (2010-10-15)

On a Bernoulli problem with geometric constraints

Antoine Laurain 1, Yannick Privat 2

(2012)

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.

1:	Humboldt University of Berlin, Department of Mathematics
	University of Graz
2:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

Research team: Analyse numérique

Subject

:

Mathematics/Analysis of PDEs

Keyword(s): free boundary problem – Bernoulli condition – shape optimization – parameterization method

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From: Yannick Privat <>

Submitted on: Wednesday, 13 October 2010 19:00:01

Updated on: Thursday, 8 March 2012 11:48:34