@article {1999,
title = {Oleinik type estimates and uniqueness for n x n conservation laws},
journal = {J. Differential Equations 156 (1999), no. 1, 26--49},
number = {SISSA;150/97/M},
year = {1999},
publisher = {Elsevier},
abstract = {Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of $u$ in a forward neighborhood of each point in the $t\\\\text{-}x$ plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleinik in the scalar case.},
doi = {10.1006/jdeq.1998.3606},
url = {http://hdl.handle.net/1963/3375},
author = {Alberto Bressan and Paola Goatin}
}