Two-Dimensional Riemann Problem for Scalar Conservation Laws

Using the generalized characteristic analysis method, we study the two-dimensional Riemann problem for scalar conservation laws, which is nonconvex along the y direction, and interactions of its elementary waves, give the classification of initial discontinuities and construct all Riemann solutions, which Riemann data are two or three pieces of constants. All kinds of Guckenheimer structure appear in the solutions and the necessary and sufficient condition of appearance of it is given.