A case study of port-Hamiltonian systems with a moving interface

TL;DR

This paper models coupled conservation law systems with a moving interface as a port-Hamiltonian system, providing stability conditions and highlighting the restrictiveness of these conditions through an example.

Contribution

It introduces a novel modeling approach for port-Hamiltonian systems with moving interfaces and analyzes their stability conditions.

Findings

Provided sufficient conditions for Kato-stability of the system.

Showed that these stability conditions are quite restrictive.

Identified open questions regarding evolution family generation.

Abstract

We model two systems of two conservation laws defined on complementary spatial intervals and coupled by a moving interface as a single non-autonomous port-Hamiltonian system, and provide sufficient conditions for its Kato-stability. An example shows that these conditions are quite restrictive. The more general question under which conditions an evolution family is generated remains open.