Well-posedness Theory for Geometry Compatible Hyperbolic Conservation Laws on Manifolds

@inproceedings{BenArtzi2008WellposednessTF,
  title={Well-posedness Theory for Geometry Compatible Hyperbolic Conservation Laws on Manifolds},
  author={Matania Ben-Artzi and Philippe G. LeFloch},
  year={2008}
}
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear 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. We… CONTINUE READING
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