Olivier Pironneau (2002)
ESAIM: Control, Optimisation and Calculus of Variations
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
Olivier Pironneau (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
Y. Smagina, M. Sheintuch (2010)
Mathematical Modelling of Natural Phenomena
We consider the stabilization of a rotating temperature pulse traveling in a continuous asymptotic model of many connected chemical reactors organized in a loop with continuously switching the feed point synchronously with the motion of the pulse solution. We use the switch velocity as control parameter and design it to follow the pulse: the switch velocity is updated at every step on-line using the discrepancy between the temperature at the front...
Rodrigo Lecaros, Lionel Rosier (2014)
ESAIM: Control, Optimisation and Calculus of Variations
In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron’s return method, we establish some local controllability...
Phuong Anh Nguyen, Jean-Pierre Raymond (2001)
ESAIM: Control, Optimisation and Calculus of Variations
We consider optimal control problems for convection-diffusion equations with a pointwise control or a control localized on a smooth manifold. We prove optimality conditions for the control variable and for the position of the control. We do not suppose that the coefficient of the convection term is regular or bounded, we only suppose that it has the regularity of strong solutions of the Navier–Stokes equations. We consider functionals with an observation on the gradient of the state. To obtain optimality...
Phuong Anh Nguyen, Jean-Pierre Raymond (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We consider optimal control problems for convection-diffusion equations with a pointwise control or a control localized on a smooth manifold. We prove optimality conditions for the control variable and for the position of the control. We do not suppose that the coefficient of the convection term is regular or bounded, we only suppose that it has the regularity of strong solutions of the Navier–Stokes equations. We consider functionals with an observation on the gradient of the state. To obtain...
Nicolas Burq, Maciej Zworski (2004)
Journées Équations aux dérivées partielles
Olivier Glass (1997/1998)
Séminaire Équations aux dérivées partielles
Jin Hai Yan (1992)
Revista Matemática de la Universidad Complutense de Madrid
Combining HUM and compactness arguments the exact controllability is prove for time dependent smooth kernels.
Nicolas Burq, Jean-Marc Schlenker (1998)
Bulletin de la Société Mathématique de France
Nicolas Burq (1993)
Mémoires de la Société Mathématique de France
Louis Roder Tcheugoué Tébou (1997)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Kim Dang Phung (2000)
ESAIM: Control, Optimisation and Calculus of Variations
Kim Dang Phung (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.
G. Lebeau (1989/1990)
Séminaire Équations aux dérivées partielles (Polytechnique)
Claude Bardos, Gilles Lebeau, Jeff Rauch (1987)
Journées équations aux dérivées partielles
G. Lebeau, L. Robbiano (1994/1995)
Séminaire Équations aux dérivées partielles (Polytechnique)
Jaffard, S. (1990)
Portugaliae mathematica
Mohamed El Alaoui Talibi, Abdellah El Kacimi (2001)
ESAIM: Control, Optimisation and Calculus of Variations
Dans ce papier, nous étudions un problème de contrôle par les coefficients issu de la lubrification élastohydrodynamique. La variable de contrôle est l’épaisseur du fluide. Le phénomène de cavitation est pris en compte par le modèle Elrod-Adams, connu pour ses performances dans la conservation des débits d’entrée et de sortie. L’idée est de régulariser dans l’équation d’état le graphe d’Heaviside, en l’approchant par une suite de fonctions monotones et régulières. Nous dérivons les conditions d’optimalité...
Mohamed El Alaoui Talibi, Abdellah El Kacimi (2010)
ESAIM: Control, Optimisation and Calculus of Variations
The purpose of this paper is to study a control by coefficients problem issued from the elastohydrodynamic lubrication. The control variable is the film thickness.The cavitation phenomenon takes place and described by the Elrod-Adams model, suggested in preference to the classical variational inequality due to its ability to describe input and output flow. The idea is to use the penalization in the state equation by approximating the Heaviside graph whith a sequence of monotone and regular functions....