Hyperbolic Conservation Laws on Manifolds: Total Variation Estimates and the Finite Volume Method

@inproceedings{Amorim2005HyperbolicCL,
  title={Hyperbolic Conservation Laws on Manifolds: Total Variation Estimates and the Finite Volume Method},
  author={Paulo Amorim and Matania Ben-Artzi and Philippe G. LeFloch},
  year={2005}
}
This paper investigates some properties of entropy solutions of hyperbolic conser- vation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) property to manifolds, by deriving conditions on the flux of the conservation law and a given vector field ensuring that the total variation of the solution along the integral curves of the vector field is non-increasing in time. Our results are next specialized to the important case of a flow on the 2-sphere, and… CONTINUE READING

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