Displaying similar documents to “On a Bernoulli problem with geometric constraints”

On a Bernoulli problem with geometric constraints

Antoine Laurain, Yannick Privat (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by  ≥ 0 and its boundary to contain a segment of the hyperplane  {  = 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...

Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini

Slim Chaabane, Mohamed Jaoua (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This work deals with a non linear inverse problem of reconstructing an unknown boundary , the boundary conditions prescribed on being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction depends only on the state ...

Motion Planning for a nonlinear Stefan Problem

William B. Dunbar, Nicolas Petit, Pierre Rouchon, Philippe Martin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider a free boundary problem for a nonlinear parabolic partial differential equation. In particular, we are concerned with the inverse problem, which means we know the behavior of the free boundary and would like a solution, a convergent series, in order to determine what the trajectories of the system should be for steady-state to steady-state boundary control. In this paper we combine two issues: the free boundary (Stefan) problem with a quadratic nonlinearity....

Global minimizer of the ground state for two phase conductors in low contrast regime

Antoine Laurain (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to and to small geometric perturbations of the optimal shape, that the global minimum of the...

Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain

Eugene Kramer, Ivonne Rivas, Bing-Yu Zhang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we study a class of Initial-Boundary Value Problems proposed by Colin and Ghidaglia for the Korteweg-de Vries equation posed on a bounded domain (0). We show that this class of Initial-Boundary Value Problems is locally well-posed in the classical Sobolev space (0) for > -3/4, which provides a positive answer to one of the open questions of Colin and Ghidaglia [6 (2001) 1463–1492].

Domain-Free -Calculus

Ken-Etsu Fujita (2010)

RAIRO - Theoretical Informatics and Applications

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We introduce a domain-free -calculus of call-by-value as a short-hand for the second order Church-style. Our motivation comes from the observation that in Curry-style polymorphic calculi, control operators such as -operators cannot, in general, handle correctly the terms placed on the control operator's left, so that the Curry-style system can fail to prove the subject reduction property. Following the continuation semantics, we also discuss the notion of values in classical...

On shape optimization problems involving the fractional laplacian

Anne-Laure Dalibard, David Gérard-Varet (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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Our concern is the computation of optimal shapes in problems involving (−). We focus on the energy (Ω) associated to the solution of the basic Dirichlet problem ( − )  = 1 in Ω,  = 0 in Ω. We show that regular minimizers Ω of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the...

Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd

M. Aurada, M. Feischl, J. Kemetmüller, M. Page, D. Praetorius (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the solution of second order elliptic PDEs in R with inhomogeneous Dirichlet data by means of an –adaptive FEM with fixed polynomial order  ∈ N. As model example serves the Poisson equation with mixed Dirichlet–Neumann boundary conditions, where the inhomogeneous Dirichlet data are discretized by use of an –stable projection, for instance, the –projection for  = 1 or the Scott–Zhang projection for general  ≥ 1. For error estimation, we use...