Published Paper

Inserted: 5 sep 2020
Last Updated: 19 nov 2022

Journal: Vietnam Journal of Mathematics
Year: 2021
Doi: https://doi.org/10.1007/s10013-021-00506-7

Abstract:

We study the exact boundary controllability of a class of nonlocal conservation laws modeling traffic flow. The velocity of the macroscopic dynamics depends on a weighted average of the traffic density ahead and the averaging kernel is of exponential type. Under specific assumptions, we show that the boundary controls can be used to steer the system towards a target final state or out-flux. The regularizing effect of the nonlocal term which leads to the uniqueness of weak solutions enables us to prove that the exact controllability is equivalent to the existence of weak solutions to the backwards-in-time problem. We also study steady states and the long-time behavior of the solution under specific boundary conditions.

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