# 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

vertices.

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.

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

vertices.

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:

35L65

Keywords: