Mixed Systems: ODEs - Balance Laws

We prove the well posedness of mixed problems consisting of
a system of ordinary differential equations coupled with systems
of balance laws in domains with moving boundaries. The inter-
faces between the systems are provided by the boundary data and
boundary positions. Various situations that fit into this framework
are studied, both analytically and numerically. We consider a piston
moving in a pipe full of fluid, a model for fluid-particle interaction
and a traffic model. References to other examples in the literature
are provided.