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Well-posedness of Networked Hyperbolic Systems of Balance Laws

  • Martin GugatEmail author
  • Michael Herty
  • Axel Klar
  • Günther Leugering
  • Veronika Schleper
Chapter
Part of the International Series of Numerical Mathematics book series (ISNM, volume 160)

Abstract

We present an overview on recent results concerning hyperbolic systems on networks. We present a summary of theoretical results on existence, uniqueness and stability. The established theory extends previously known results on the Cauchy problem for nonlinear, 2×2 hyperbolic balance laws. The proofs are based on Wave-Front Tracking and therefore we present detailed results on the Riemann problem first.

Keywords

Hyperbolic conservation laws on networks optimal control of networked systems management of fluids in pipelines 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Martin Gugat
    • 1
    Email author
  • Michael Herty
    • 2
  • Axel Klar
    • 3
  • Günther Leugering
    • 1
  • Veronika Schleper
    • 4
  1. 1.Department of MathematicsUniversity of Erlangen–NürnbergErlangenGermany
  2. 2.Department of MathematicsRWTH Aachen UniversityAachenGermany
  3. 3.Department of MathematicsTU KaiserslauternKaiserslauternGermany
  4. 4.Department of MathematicsUniversity of StuttgartStuttgartGermany

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