Control for the sine-gordon equation
Laboratoire d'Analyse Numérique,
Université de Paris–Sud, Orsay, France; firstname.lastname@example.org.
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.
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