### One Sided Estimates and Uniqueness for Hyperbolic Systems of Balance Laws

Paola Goatin

Abstract: Uniqueness of solutions of genuinely nonlinear $n\times n$ strictly hyperbolic systems of balance laws is established moving from a refined version of the Ole\u\i nik-type decay estimates found in [*]. As middle step, the result relies on the fulfillment of a condition which controls the local oscillation of the solution in a forward neighborhood of each point in the $t$-$x$ plane.

[*] P. Goatin and L. Gosse, Decay of Positive Waves for $n \times n$ Hyperbolic Systems of Balance Laws, Preprint 2001-046.

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Author(s):
Paola Goatin, <goatin@cmapx.polytechnique.fr>
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