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

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.