Conservation Laws with Discontinuous Flux Functions

Part of the Applied Mathematical Sciences book series (AMS, volume 152)


In one spatial dimension, a conservation law with a space-dependent flux can be written
$$\displaystyle u_{t}+f(x,u)_{x}=0,\quad x\in\mathbb{R},\quad t> 0.$$
Since the interpretation of f is the flux of u at the point x, there are many applications where the flux depends on the location. We give some simple examples that are modeled by such conservation laws.


Weak Solution Travel Wave Solution Riemann Problem Entropy Solution Entropy Condition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of MathematicsUniversity of OsloOsloNorway

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