Controllability for a One-Dimensional Wave Equation in a Non-cylindrical Domain
- 16 Downloads
This paper deals with the controllability for a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. This equation models small vibrations of a string where an endpoint is fixed and the other is moving. As usual, we consider one main control (the leader) and an additional secondary control (the follower). We use Stackelberg–Nash strategies.
KeywordsWave equation hierarchic control Stackelberg–Nash strategy controllability
Mathematics Subject Classification35Q10 35B37 35B40
The author wants to express his gratitude to the anonymous reviewers for their questions and commentaries; they were very helpful in improving this article.
- 2.Díaz, J., Lions, J.-L.: On the approximate controllability of Stackelberg–Nash strategies. In: Díaz, J.I. (ed.) Ocean Circulation and Pollution Control Mathematical and Numerical Investigations, 17–27. Springer, Berlin (2005)Google Scholar
- 18.Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton (1969)Google Scholar