On $2\times2$ Conservation Laws at a Junction
Authors:
- R. M. ColomboRCR. M. Colombo
- M. HertyMHM. Herty
- V. SachersVSV. Sachers
- 1 January 2008
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 40 (2) , 605-622
Abstract
This paper deals with $2\times 2$ conservation laws at a junction. For the Cauchy problem, existence, uniqueness, and Lipschitz continuous dependence of the solution from the initial data as well as from the conditions at the junction are proved. The present construction comprehends the case of the p-system used to describe gas flow in networks and hereby unifies different approaches present in the literature. Furthermore, different models for water networks are considered.
Keywords
This publication has 21 references indexed in Scilit:
- On the Cauchy Problem for the p-System at a JunctionSIAM Journal on Mathematical Analysis, 2008
- Lyapunov stability analysis of networks of scalar conservation lawsNetworks and Heterogeneous Media, 2007
- A Well Posed Riemann Problem for the $p$--System at a JunctionNetworks and Heterogeneous Media, 2006
- Gas flow in pipeline networksNetworks and Heterogeneous Media, 2006
- Optimization criteria for modelling intersections of vehicular traffic flowNetworks and Heterogeneous Media, 2006
- Stability of the Riemann semigroup with respect to the kinetic conditionQuarterly of Applied Mathematics, 2004
- Global boundary controllability of the de St. Venant equations between steady statesAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 2003
- Sonic Hyperbolic Phase Transitions and Chapman-Jouguet DetonationsJournal of Differential Equations, 2002
- On the stability of the standard Riemann semigroupProceedings of the American Mathematical Society, 2002
- On the Front-Tracking AlgorithmJournal of Mathematical Analysis and Applications, 1998