AI 中文总结
本研究将带不连续通量的守恒律首次应用于交通流，引入改进黎曼求解器并推广弱解存在性理论，还为含自由流的两相模型构造求解器并证明弱解存在。
AI 中文摘要
本研究对文献\uc81b{ABS2025}中提出的模型进行交通流解读，将带不连续、依赖梯度的通量的守恒律适配至宏观交通场景，假设在密度域\uc81b{[0,u_max]}上定义了凹通量函数\uc81b{f(u)}和\uc81b{g(u)}；为避免违反最大密度约束，引入适配该场景的改进黎曼求解器，并推广文献\uc81b{ABS2025}中建立的弱解存在性理论；最终，为包含自由流状态的更广泛两相模型构造黎曼求解器，其中在\uc81b{[0,u_max]}的一个子集上满足\uc81b{f(u)=g(u)}，并在该更一般框架下证明弱解的存在性。
英文摘要
This work provides a traffic flow interpretation of the model recently introduced in \cite{ABS2025}. We adapt the conservation law with discontinuous gradient-dependent flux to a macroscopic traffic setting, assuming concave flux functions $f(u)$ and $g(u)$ defined on the density domain $[0,u_{\max}]$. To prevent violations of the maximal density constraint, we introduce modified Riemann Solvers tailored to this setting and generalize the existence theory for weak solutions developed in \cite{ABS2025}. Finally, we construct Riemann Solvers for a broader two-phase model incorporating a free-flow regime, in which $f(u)=g(u)$ on a subset of $[0,u_{\max}]$, and establish existence of weak solutions in this more general framework.
