%0 Journal Article
%J J. Differential Equations 156 (1999), no. 1, 26--49
%D 1999
%T Oleinik type estimates and uniqueness for n x n conservation laws
%A Alberto Bressan
%A Paola Goatin
%X 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 Oleĭnik in the scalar case.
%B J. Differential Equations 156 (1999), no. 1, 26--49
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/3375
%1 955
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-01T09:26:02Z\\nNo. of bitstreams: 1\\nOleinik_type.pdf: 1567166 bytes, checksum: ba588e7f2b587d26f5b613a53557bb2f (MD5)
%R 10.1006/jdeq.1998.3606