The Cauchy problem at a node with buffer

Mauro Garavello (1) , Paola Goatin (2)

1 DISTA - Dipartimento di Scienze e Tecnologie Avanzate
2 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE

We consider the Lighthill-Whitham-Richards traffic flow model on a network composed by an arbitrary number of incoming and outgoing arcs connected together by a node with a buffer. Similar to [M. Herty, J.-P. Lebacque, and S. Moutari. A novel model for intersections of vehicular traffic flow. Netw. Heterog. Media, 4(4):813–826 (electronic), 2009], we define the solution to the Riemann problem at the node and we prove existence and well posedness of solutions to the Cauchy problem, by using the wave-front tracking technique and the generalized tangent vectors.

Domains: Analysis of PDEs [math.AP]

Mauro Garavello, Paola Goatin. The Cauchy problem at a node with buffer. Discrete and Continuous Dynamical Systems - Series A, 2012. ⟨inria-00556954⟩