ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - October 2011 - Volume 17 - Issue 04

Research Articles

 
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Gilles Aubert and Daniele Graziani

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 909 - 930

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010029 (About DOI)

 

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Luise Blank, Martin Butz and Harald Garcke

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 931 - 954

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010032 (About DOI)

 

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Elena Bonetti and Michel Frémond

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 955 - 974

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010033 (About DOI)

 

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Hongwei Lou

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 975 - 994

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010034 (About DOI)

 

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Deterministic state-constrained optimal control problems without controllability assumptions

 
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Olivier Bokanowski, Nicolas Forcadel and Hasnaa Zidani

In the setting of optimal control problems of ordinary differential equations with state constraints, the paper aims at characterizing the value function using the Hamilton-Jacobi-Bellamn (HJB) equation. The answer is known when one assumes either the inward or the outward pointing qualification condition. In the present paper no controllability assumption is done. The value function can be discontinuous and the problem may be unfeasible, resulting in an infinite value function.

A first reduction consists in mapping the real line to a bounded interval, after which to an unfeasible problem is associated the value say 1. It appears then that the value function is the unique solution of the HJB equation with some elaborated boundary conditions. In order to get a more practical characterization (especially when having in view numerical methods), the authors consider the HJB equation on a slightly enlarged domain, with 'classical' boundary conditions. They show that any l.s.c. bounded viscosity solution of the latter converges punctually to the original value function.

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 995 - 1015

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010030 (About DOI)

 

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Mark Asch, Marion Darbas and Jean-Baptiste Duval

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1016 - 1034

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010031 (About DOI)

 

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Alessandro Giacomini and Alessandro Musesti

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1035 - 1065

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010036 (About DOI)

 

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Marc Briane and Juan Casado-Díaz

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1066 - 1087

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010037 (About DOI)

 

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On the null-controllability of diffusion equations

 
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Gérald Tenenbaum and Marius Tucsnak

Controllability of Partial Differential Equations is a very active research field in the recent decades, especially after the classical paper by J.-L. Lions (SIAM Rev., 1988). In particular, H.O. Fattorini and D.L. Russell (1972) addressed the null controllability of linear parabolic equations in one space dimension, while the same controllability result in several space dimensions has been independently established by G. Lebeau and L. Robbiano (1995), and by A.V. Fursikov and O.Yu. Imanuvilov (1996). This article introduces a new abstract version of the Lebeau and Robbiano approach. In the special case of the heat equation in high dimensional rectangular domains, the authors provide an impressive alternative way, based on an inequality of P. Turan (1946), to check the key Lebeau-Robbiano spectral condition so that the corresponding null controllbility can be proved without using the usual Carleman-type estimate.

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1088 - 1100

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010035 (About DOI)

 

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Scott W. Hansen and Oleg Imanuvilov

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1101 - 1132

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010040 (About DOI)

 

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Carlo Mariconda and Giulia Treu

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1133 - 1143

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010038 (About DOI)

 

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Jean-François Couchouron

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1144 - 1157

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010041 (About DOI)

 

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Marta Lewicka and Mohammad Reza Pakzad

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1158 - 1173

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010039 (About DOI)

 

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Liangquan Zhang and Yufeng Shi

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1174 - 1197

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010042 (About DOI)

 

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Otared Kavian and Oumar Traoré

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 04 / 2011, pp 1198 - 1213

© EDP Sciences, SMAI, 2010

Published online by Cambridge University Press: 19 January 2011

DOI: http://dx.doi.org/10.1051/cocv/2010043 (About DOI)

 

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