  This thesis deals with the formulation and analysis of two systems of
conservation laws defined on two complementary intervals and coupled by some
moving interface as a single infinite-dimensional port-Hamiltonian system. This
approach may be regarded as an extension of the well-established mathematical
framework of boundary port-Hamiltonian systems, i.e., infinite-dimensional
Hamiltonian systems interacting with its physical environment. In order to keep
track of the power flow at the position of the interface, we introduce
interface port variables. We provide a well-posed port-Hamiltonian model of two
distinct systems of conservation laws defined on two complementary,
1-dimensional spatial domains that are coupled by a fixed interface, and
illustrate this result by reference to two transmission lines coupled through a
resistor. Furthermore, we discuss under which boundary and interface conditions
this system is exponentially stable. Since the formulation in case of a moving
interface is quite troubled, we present some results that may be regarded as a
first step towards a well-posed model, and debate the main issues that have to
be tackled in the future.
