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We utilize a three-dimensional manifold to solve Riemann Problems that arisefrom a system of two conservation laws with quadratic flux functions. Points inthis manifold represent potential shock waves, hence its name wave manifold.This manifold is subdivided into regions according to the Lax admissibilityinequalities for shocks. Finally, we present solutions for the Riemann Problemsfor various cases and exhibit continuity relative to $L$ and $R$ data, despitethe fact that the system is not strictly hyperbolic. The usage of this manifoldregularizes the solutions despite the presence of an elliptic region.

Decomposition of the Wave Manifold into Lax Admissible Regions and its Application to the Solution of Riemann Problems