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Control for the sine-gordon equation

Published online by Cambridge University Press:  15 October 2004

Madalina Petcu  and
Roger Temam
Madalina Petcu
Affiliation:
Laboratoire d'Analyse Numérique, Université de Paris–Sud, Orsay, France; madalina.petcu@math.u-psud.fr. The Institute of Mathematics of the Romanian Academy, Bucharest, Romania.
Roger Temam
Affiliation:
Laboratoire d'Analyse Numérique, Université de Paris–Sud, Orsay, France; madalina.petcu@math.u-psud.fr. The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA.
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Abstract

In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.

Keywords

Robust controlsine-Gordon equationenergy estimatessaddle point.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 4 , October 2004 , pp. 553 - 573
Copyright
© EDP Sciences, SMAI, 2004

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