Boundary Port Hamiltonian systems of conservation laws coupled by a moving interface

In this paper we consider the port-Hamiltonian formulation of systems of two conservation laws defined on two complementary intervals of some interval of the real line and coupled by some moving interface. We recall first how two port Hamiltonian systems coupled by an interface may be expressed as an port Hamiltonian systems augmented with two variables being the characteristic functions of of two spatial domains. Then we consider the case of a moving interface and show that it may be expressed as the preceeding port Hamiltonian system augmented with an input, being the velocity of the interface and define a conjugated output variable. We conclude by giving some definition of the passivity of interface relations coupling the external variables associated with the interface.