ON THE UNIQUENESS OF ENTROPY SOLUTIONSTO THE RIEMANN PROBLEM FOR 2 x 2 HYPERBOLIC SYSTEMSOF CONSERVATION LAWS

摘要

In this paper we revisit the Riemann problem for 2 x 2 hyperbolic systems of con-servation laws, which satisfy the condition that the product of non-diagonal elements in the Frechetderivative (Jacobian) of the flux is positive, the genuine nonlinearity condition, and the Smoller-Johnson condition in one space variable. The first condition implies that the system is strictlyhyperbolic. By developing the shock curve approach, we give an alternative shock curve approachand re-prove the uniqueness of self-similar solutions satisfying the Lax entropy condition at discon-tinuities.