Well-posedness of linear first order Port-Hamiltonian Systems on multidimensional spatial domains

Abstract

We consider a port-Hamiltonian system on a spatial domain $\Omega \subseteq {\mathbb{R}}^n$ that is bounded with Lipschitz boundary. We show that there is a boundary triple associated to this system. Hence, we can characterize all boundary conditions that provide unique solutions that are non-increasing in the Hamiltonian. As a by-product we develop the theory of quasi Gelfand triples. Adding ``natural'' boundary controls and boundary observations yields scattering/impedance passive boundary control systems. This framework can be applied to the wave equation, Maxwell equations and Mindlin plate model, and probably many more.

References in corpus (2)

• Port-Hamiltonian formulation and symplectic discretization of Plate models. Part I : Mindlin model for thick plates
• Linear wave systems on $n$-D spatial domains

Cited by in corpus (7)

• Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus
• Second order systems on Hilbert spaces with nonlinear damping
• Semi-uniform stabilization of anisotropic Maxwell's equations via boundary feedback on split boundary
• Quasi Gelfand triples
• Random acoustic boundary conditions and Weyl's law for Laplace-Beltrami operators on non-smooth boundaries
• Weak equals strong L2 regularity for partial tangential traces on Lipschitz domains
• Well-posedness and stability of the Lagrange representation of the n-D wave equation via boundary triples