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Issue ESAIM: COCV
Volume 10, Number 4, October 2004
Page(s) 553 - 573
DOI 10.1051/cocv:2004020

ESAIM: COCV, October 2004, Vol. 10, pp. 553-573
DOI: 10.1051/cocv:2004020

Control for the sine-gordon equation

Madalina Petcu1, 2 and Roger Temam1, 3

1  Laboratoire d'Analyse Numérique, Université de Paris-Sud, Orsay, France; madalina.petcu@math.u-psud.fr.
2  The Institute of Mathematics of the Romanian Academy, Bucharest, Romania.
3  The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA.


(Received May 10, 2003. Revised October 2, 2003.)

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.


Mathematics Subject Classification. 35Q53, 49J20, 49J50, 49K20.

Key words: Robust control, sine-Gordon equation, energy estimates, saddle point.


© EDP Sciences, SMAI 2004


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