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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 5
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Articles

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

Pages 1008-1027 | Received 16 Jul 2011, Accepted 20 Nov 2011, Published online: 16 Dec 2011
 

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.

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