Infinite-dimensional port-Hamiltonian systems with a stationary interface

TL;DR

This paper studies infinite-dimensional port-Hamiltonian systems with a stationary interface, characterizing boundary conditions for stability and illustrating with coupled acoustic waveguides.

Contribution

It provides a characterization of boundary and interface conditions ensuring well-posedness and stability for coupled port-Hamiltonian systems with a stationary interface.

Findings

Boundary conditions for contraction semigroup generation identified.

Sufficient conditions for exponential stability established.

Application demonstrated on coupled acoustic waveguides.

Abstract

We consider two systems of two conservation laws that are defined on complementary, one-dimensional spatial intervals and coupled by an interface as a single port-Hamiltonian system. In case of a fixed interface position, we characterize the boundary and interface conditions for which the associated port-Hamiltonian operator generates a contraction semigroup. Furthermore, we present sufficient conditions for the exponential stability of the generated $C_0$-semigroup. The results are illustrated by the example of two acoustic waveguides coupled by a membrane interface.