Conservation laws on networks

Thursday, July 30, 2009 - 2:00pm - 2:50pm
EE/CS 3-180
Mauro Garavello (Università del Piemonte Orientale Amedeo Avogadro)
In this talk we consider a conservation law (or a system of conservation
laws) on a network consisting in a finite number of arcs and vertices.
This setting is justified by various applications, such as car traffic,
gas pipelines, data networks, supply chains, blood circulation and so on.
The key point in the extension of conservation laws on networks is to
define solutions at vertices. Indeed, it is sufficient to define
solutions only for Riemann problems at vertices, i.e. Cauchy problems
with constant initial data in each arc of the junction. We present some
different possibilities to produce solutions to Riemann problems at
Moreover we consider the general Cauchy problem on the network. We
explain how to prove existence of a solution both in the scalar case and
in the case of systems. In particular, for the scalar case, we introduce
general properties on Riemann solvers at vertices, which permit to have
existence of solutions for the Cauchy problem.
MSC Code: