Abstract

We consider the Riemann problem for non-genuinely nonlinear conservation laws where the flux function admits two inflection points. This is a simplification of van der Waals fluid pressure, which can be seen as a function of the specific volume for a specific entropy at which the system lacks the non-genuine nonlinearity. Corresponding to each inflection point, a nonclassical Riemann solver can be uniquely constructed. Furthermore, two kinetic relations can be used to construct nonclassical Riemann solutions.