Preprint 1998-033

A Uniqueness Condition for Hyperbolic Systems of Conservation Laws

Alberto Bressan and Marta Lewicka

Abstract: Consider the Cauchy problem for a hyperbolic $n\times n$ system of conservation laws in one space dimension: $$u_t+f(u)_x=0, u(0,x)=\bar u(x).\eqno(CP)$$ Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions $u=u(t,x)$ which have bounded variation along a suitable family of space-like curves.

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A uniqueness condition for hyperbolic systems of conservation laws
Alberto Bressan, <>
Marta Lewicka, <>
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<> August 12 1998.

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