TY - JOUR
T1 - Oleinik type estimates and uniqueness for n×n conservation laws
AU - Bressan, Alberto
AU - Goatin, Paola
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1999/7/20
Y1 - 1999/7/20
N2 - Let ut+f(u)x=0 be a strictly hyperbolic n×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-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.
AB - Let ut+f(u)x=0 be a strictly hyperbolic n×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-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.
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U2 - 10.1006/jdeq.1998.3606
DO - 10.1006/jdeq.1998.3606
M3 - Article
AN - SCOPUS:0033587469
VL - 156
SP - 26
EP - 49
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 1
ER -