Comparison among different notions of solution for the $p$-system at a junction

Rinaldo M. Colombo; Mauro Garavello

doi:10.3934/proc.2009.2009.181

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2009, Volume 2009: 181-190. Doi: 10.3934/proc.2009.2009.181 open access

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Comparison among different notions of solution for the $p$-system at a junction

Rinaldo M. Colombo^1, and
Mauro Garavello^2,

1.
Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia
2.
Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale “A. Avogadro”, Via Bellini 25/G, 15100 Alessandria

Received: July 2008

Revised: March 2009

Published: September 2009

Abstract / Introduction Related Papers Cited by

Abstract

We consider $n$ tubes exiting a junction and filled with a non viscous isentropic or isothermal fluid. In each tube a copy of the $p$-system in Euler coordinates is considered. The aim of the presentation is to compare three different notions of solutions at the junctions: p-solutions, Q-solutions and P-solutions.

Keywords:

$p$-System,
Hyperbolic Systems of Conservation Laws,
Riemann Problem,
Compressible Fluids,
Gas Dynamics.

Mathematics Subject Classification: Primary: 35L65; Secondary: 76N10.

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