On an Inverse Problem of the Generalized Bathtub Model of Network Trip Flows
<|reference_start|>On an Inverse Problem of the Generalized Bathtub Model of Network Trip Flows: In this work, we investigate the generalized bathtub model, a nonlocal transport equation for describing network trip flows served by privately operated vehicles inside a road network. First, we establish the well-posedness of the mathematical model for both classical and weak solutions. Then we consider an inverse source problem of the model with model parameters embodying particular traffic situations. We establish a conditional Lipschitz stability of the inverse problem under suitable a priori regularity assumption on the problem data, using a Volterra integral formulation of the problem. Inspired by the analysis, we develop an easy-to-implement numerical method for reconstructing the flow rates, and provide the error analysis of the method. Further we present several numerical experiments to complement the theoretical analysis.<|reference_end|>
@article{huang2024on,
    title={On an Inverse Problem of the Generalized Bathtub Model of Network Trip
  Flows},
    author={Kuang Huang, Bangti Jin, Zhi Zhou},
    journal={arXiv preprint arXiv:2409.00619},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.00619},
    primaryClass={math.AP cs.NA math.NA}
}