Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds

@article{BenArtzi2006WellposednessTF,
  title={Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds},
  author={Matania Ben-Artzi and Philippe G. LeFloch},
  journal={Annales De L Institut Henri Poincare-analyse Non Lineaire},
  year={2006},
  volume={24},
  pages={989-1008}
}
  • Matania Ben-Artzi, Philippe G. LeFloch
  • Published 2006
  • Mathematics
  • Annales De L Institut Henri Poincare-analyse Non Lineaire
  • Abstract Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to non-linear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of the conservation laws is viewed as a vector-field on the manifold and depends on the unknown function as a parameter. We introduce notions of entropy solutions in the class of bounded measurable functions and in the class of measure-valued mappings… CONTINUE READING

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