Communications in Mathematical Sciences
Volume 9 (2011)
On the uniqueness of entropy solutions to the Riemann problem for 2×2 hyperbolic systems of conservation laws
Pages: 161 – 185
In this paper we revisit the Riemann problem for 2×2 hyperbolic systems of conservation laws, which satisfy the condition that the product of non-diagonal elements in the Fréchet derivative (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 strictly hyperbolic. By developing the shock curve approach, we give an alternative shock curve approach and re-prove the uniqueness of self-similar solutions satisfying the Lax entropy condition at discontinuities.
conservation laws, the Riemann problem, shock approach
2010 Mathematics Subject Classification
35L65, 35L67, 58J45