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 interfaces 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.