We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate solutions constructed by Lax-Friedrich and Hilliges-Weidlich schemes, while the L1 stability with respect to the initial data and the delay parameter relies on a Kruzkov-type doubling of variable technique.Numerical tests are provided to illustrate the efficiency of the proposed schemes, as well as the solution dependence on the delay and look-ahead parameters.
翻译:我们证明了带时间延迟的标量非局部交通流模型弱熵解的适定性。通过Lax-Friedrich和Hilliges-Weidlich格式构造的有限体积近似解的收敛性得到存在性,而关于初始数据和延迟参数的L1稳定性则依赖于Kruzkov型双变量技术。数值实验展示了所提格式的效率,以及解对延迟和前视参数的依赖关系。