One Sided Estimates and Uniqueness for Hyperbolic Systems of Balance
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
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- Paola Goatin,
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May 6 2002.
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