Preprint 1998-032

On the Cauchy Problem for Nonlinear Hyperbolic Systems

Alberto Bressan

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.

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On the Cauchy problem for nonlinear hyperbolic systems
Alberto Bressan, <>
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<> August 11 1998.

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