TY - JOUR
T1 - Oleinik type estimates and uniqueness for n x n conservation laws
JF - J. Differential Equations 156 (1999), no. 1, 26--49
Y1 - 1999
A1 - Alberto Bressan
A1 - Paola Goatin
AB - 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.
PB - Elsevier
UR - http://hdl.handle.net/1963/3375
U1 - 955
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -