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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.
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.