## UC Berkeley / Lawrence Berkeley Laboratory

#### On the Existence of Solution of a Strongly Coupled PDE-ODE with Moving Bottleneck and Discontinuity in the Flux

**Hossein Nick Zinat Matin, UC Berkeley**

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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.
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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.
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