| Issue |
ESAIM: COCV
Volume 10, Number 4, October 2004
|
|
|---|---|---|
| Page(s) | 553 - 573 | |
| DOI | https://doi.org/10.1051/cocv:2004020 | |
| Published online | 15 October 2004 | |
Control for the sine-gordon equation
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:
10
May
2003
Revised:
2
October
2003
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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