July  2000, 6(3): 673-682. doi: 10.3934/dcds.2000.6.673

A uniqueness condition for hyperbolic systems of conservation laws

1. 

S.I.S.S.A., Via Beirut, 2-4, 34014 Trieste

2. 

SISSA, via Beirut 2-4, 34014 Trieste, Italy

Received  December 1999 Revised  March 2000 Published  April 2000

Consider the Cauchy problem for a hyperbolic $n\times n$ system of conservation laws in one space dimension:

$u_t + f(u)_x = 0$,   $u(0,x)=\bar u (x).$       $(CP)$

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.

Citation: Alberto Bressan, Marta Lewicka. A uniqueness condition for hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 673-682. doi: 10.3934/dcds.2000.6.673
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