TY - JOUR
T1 - A Remark on the Uniqueness of Solutions to Hyperbolic Conservation Laws
AU - Bressan, Alberto
AU - De Lellis, Camillo
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.
PY - 2023/12
Y1 - 2023/12
N2 - Given a strictly hyperbolic n× n system of conservation laws, it is well known that there exists a unique Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation, which are limits of vanishing viscosity approximations. The aim of this note is to prove that every weak solution taking values in the domain of the semigroup, and whose shocks satisfy the Liu admissibility conditions, actually coincides with a semigroup trajectory.
AB - Given a strictly hyperbolic n× n system of conservation laws, it is well known that there exists a unique Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation, which are limits of vanishing viscosity approximations. The aim of this note is to prove that every weak solution taking values in the domain of the semigroup, and whose shocks satisfy the Liu admissibility conditions, actually coincides with a semigroup trajectory.
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U2 - 10.1007/s00205-023-01936-y
DO - 10.1007/s00205-023-01936-y
M3 - Article
AN - SCOPUS:85175537324
SN - 0003-9527
VL - 247
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 6
M1 - 106
ER -