We couple, at a fixed interface, the microscopic Follow the Leader model and the macroscopic Lighthill–Whitham–Richards model, both used for describing vehicular traffic. The coupling is obtained by suitable boundary conditions. We prove existence of solutions for the corresponding Cauchy problem, by using the wave-front tracking method and classical results on ordinary differential equations.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Coupling conditions
- Follow the Leader model
- Lighthill–Whitham–Richards model
- Traffic models