Title: On an Inverse Problem of the Generalized Bathtub Model of Network Trip Flows Show Chinese title

Title: 关于广义浴缸模型网络行程流的逆问题

Abstract: 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. Show Chinese abstract

Abstract: 在本工作中，我们研究了广义浴缸模型，这是一个非局部输运方程，用于描述道路网络内由私人运营车辆提供的网络行程流量。 首先，我们建立了经典解和弱解的数学模型的适定性。 然后，我们考虑了模型的逆源问题，其中模型参数体现了特定的交通情况。 在对问题数据进行适当先验正则性假设的情况下，我们利用问题的Volterra积分形式建立了逆问题的条件Lipschitz稳定性。 受分析的启发，我们开发了一种易于实现的数值方法来重建流量速率，并提供了该方法的误差分析。 此外，我们进行了几个数值实验以补充理论分析。