<<<<<<< Updated upstream From an application point of view, coupled PDE-ODE problems have various applications in science and engineering including blood flow, and modern mobility. From a theoretical point of view, these problems show complex behavior which stem from the interactions of waves and creation of non-classical shocks. In this talk, we analyze such a PDE-ODE model with discontinuity in the flux as well as a flux constraint. We discuss the analytical complexities of the model and by proposing a modified Riemann solution we prove the existence of weak solutions to the Cauchy problem using the wavefront tracking scheme. ======= From application point of view, coupled PDE-ODE problems have various applications in science and engineering including blood flow, and modern mobility. From a theoretical point of view, these problems show complex behavior which stem from the interactions of waves and creation of non-classical shocks. In this talk, we analyze such a PDE-ODE model with discontinuity in the flux as well as a flux constraint. We discuss the analytical complexities of the model and by proposing a modified Riemann solution we prove the existence of weak solutions to the Cauchy problem using the wavefront tracking scheme. >>>>>>> Stashed changes