Well-posedness of Networked Hyperbolic Systems of Balance Laws

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


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.


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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