Existence of solutions to the Riemann problem for 2 × 2 conservation laws

Abstract

We consider the Riemann problem for a class of 2 × 2 systems of conservation laws which do not satisfy the strictly hyperbolicity condition. Our main assumption is that the product of non-diagonal elements within the Fŕechet derivative (Jacobian) of the flux is nonnegative. By improving a vanishing viscosity approach, we establish the existence of solutions to the Riemann problem for those systems.

Keywords:

• conservation laws
• Riemann problem
• existence theorem

AMS Subject Classifications::

• 35L45
• 35L65