On the uniqueness of solutions to hyperbolic systems of conservation laws

For general hyperbolic systems of conservation laws we show that dissipative weak solutions belonging to an appropriate Besov space B q ? , ? and satisfying a one-sided bound condition are unique within the class solutions. The exponent > 1 / 2 is universal independently nature nonlinearity regularity need only be imposed in when system expressed variables. proof utilises commutator estimate which allows for extension relative entropy method required setting. elasticity, shallow water magnetohydrodynamics, isentropic Euler investigated, recovering recent results latter. Moreover, article explores triangular motivated by studies chromatography constructs explicit solution fails Lipschitz, yet satisfies conditions presented uniqueness result.