Linear wave systems on $n$-D spatial domains
Mikael Kurula, Hans Zwart
TL;DR
This paper analyzes the linear wave equation in n-dimensional domains, characterizing boundary conditions for energy conservation and formulating it as a boundary control system with inputs and outputs.
Contribution
It introduces a boundary triplet framework for the undamped wave equation and characterizes energy-preserving boundary conditions, extending to boundary control systems.
Findings
Boundary triplet associated with the undamped wave equation
Characterization of boundary conditions for energy non-increasing solutions
Formulation of the wave system as an impedance conservative boundary control system
Abstract
In this paper we study the linear wave equation on an -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.
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