ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - October 2004 - Volume 10, Issue 04  

Research Article

Control for the sine-gordon equation

Petcu, Madalinaa1a2 and Temam, Rogera1a3

a1 Laboratoire d'Analyse Numérique, Université de Paris–Sud, Orsay, France; madalina.petcu@math.u-psud.fr.

a2 The Institute of Mathematics of the Romanian Academy, Bucharest, Romania.

a3 The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA.

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.

(Received May 10 2003)

(Revised October 2 2003)

(Online publication October 15 2004)

Key Words:

  • Robust control;
  • sine-Gordon equation;
  • energy estimates;
  • saddle point.

Mathematics Subject Classification:

  • 35Q53;
  • 49J20;
  • 49J50;
  • 49K20