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.