Time-varying Riemann solvers for conservation laws on networks
This paper deals with a scalar partial differential equation in conservation form on a network, composed by a finite collection of arcs connected together at nodes. To describe the dynamics, it is sufficient to define solutions to Riemann problems at nodes, which are Cauchy problems with constant initial conditions on the arcs meeting at the node. Using the same terminology of conservation laws on Euclidean spaces, the maps providing such solutions are called Riemann solvers at nodes. The authors prove existence of solutions to Cauchy problems on the whole network.
scientific article; zbMATH DE number 5566230
scientific article