Abstract: This paper consider various examples of metrics which are contractive w.r.t.~an evolution semigroup, and discusses the possibility of an abstract O.D.E.~theory on metric spaces, with applications to hyperbolic systems. In particular, using a recently introduced definition of Viscosity Solutions, it is shown how a strictly hyperbolic system of conservation laws can be reformulated as an abstract evolution equation on a closed domain of $BV$ functions, with the $L^1$ distance.
mailto:conservation@math.ntnu.no Last modified: Tue Aug 11 12:08:21 1998