Solving 1D Conservation Laws Using Pontryagin’s Minimum Principle

@article{Kang2017Solving1C,
  title={Solving 1D Conservation Laws Using Pontryagin’s Minimum Principle},
  author={Wei Kang and Lucas C. Wilcox},
  journal={Journal of Scientific Computing},
  year={2017},
  volume={71},
  pages={144-165}
}
  • Wei Kang, Lucas C. Wilcox
  • Published 2017
  • Mathematics, Computer Science
  • Journal of Scientific Computing
  • This paper discusses a connection between scalar convex conservation laws and Pontryagin’s minimum principle. For flux functions for which an associated optimal control problem can be found, a minimum value solution of the conservation law is proposed. For scalar space-independent convex conservation laws such a control problem exists and the minimum value solution of the conservation law is equivalent to the entropy solution. This can be seen as a generalization of the Lax–Oleinik formula to… CONTINUE READING

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