Linear wave systems on n-D spatial domains

Abstract

In this paper, we study the linear wave equation on an n-dimensional spatial domain. We show that there is a boundary triplet associated to the undamped wave equation. This enables us to characterise all boundary conditions for which the undamped wave equation possesses a unique solution non-increasing in the energy. Furthermore, we add boundary inputs and outputs to the system, thus turning it into an impedance conservative boundary control system.

Keywords:

• wave equation
• boundary triplet
• boundary control

Acknowledgments

Part of this research was carried out while the first author was visiting the University of Twente in 2011–12. The authors would also like to thank the anonymous referees for their most constructive remarks which improved the paper significantly.

Additional information

Funding

The first author gratefully acknowledges financial support by Ruth och Nils-Erik Stenbäcks stiftelse.