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A uniqueness condition for hyperbolic systems of conservation laws

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  • 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.

    Mathematics Subject Classification: 35L65, 35L45.


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