ABSTRACT
This chapter provides the Riemann probem for scalar conservation laws with the generalized characteristic method. It facilitates the understanding of the Rankine-Hugoniot relation and the verification of the entropy condition of shocks so as to make it easier to construct the Riemann solutions considered. The chapter develops the method of generalized characteristic analysis to construct the solutions of the Riemann problem for scalar conservation laws in two space variables. The types of exterior waves are closely linked to the relative position of the singularity curves and the corresponding initial discontinuity. This chapter is devoted to the four-wave Riemann problem, for which the initial data is assumed to be constant in each quadrant.
