多车道交通模型的非局部方法
Nonlocal approaches for multilane traffic models
摘要：
提出了一个基于平衡定律的多车道交通模型，其中非局部源项用于描述车道变换率。建模框架包括考虑本地和非本地通量函数。基于Goddom型数值格式，我们给出了BV估计和一个离散熵不等式.结合$L^1$ -压缩性，证明了该方程弱解的存在唯一性.数值算例表明，与局部通量函数和局部源相比，非局部影响。
英文摘要：
We present a multilane traffic model based on balance laws, where the nonlocal source term is used to describe the lane changing rate. The modelling framework includes the consideration of local and nonlocal flux functions. Based on a Godunov type numerical scheme, we provide BV estimates and a discrete entropy inequality. Together with the $L^1$-contractivity property, we prove existence and uniqueness of weak solutions. Numerical examples show the nonlocal impact compared to local flux functions and local sources.
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