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Coupling of Systems of Hyperbolic Equations
Author(s) -
Herty Michael
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510309
Subject(s) - conservation law , dimension (graph theory) , extension (predicate logic) , coupling (piping) , nonlinear system , space (punctuation) , hyperbolic partial differential equation , flow (mathematics) , mathematics , mathematical analysis , pure mathematics , computer science , physics , partial differential equation , geometry , engineering , mechanical engineering , quantum mechanics , programming language , operating system
We consider the Aw‐Rascle system of hyperbolic equations which describes traffic flow phenomena on a single road. The model consists of two coupled nonlinear conservation laws in a single space dimension. We study an extension of the Aw/Rascle system to a network of roads. We derive necessary coupling conditions and introduce an obvious definition of a solution. We prove the existence of a solution to the road network problem. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)