Non-selfsimilar solutions for a hyperbolic system of conservation laws in two space dimensions

The non-selfsimilar Riemann problem for a two-dimensional nonstrictly hyperbolic system of conservation laws is considered, where the initial data are two constant states separated by a smooth curve. Without dimension reduction or coordinate transformation, the two-dimensional global solutions are constructed for six cases according to the normal velocities on both sides of the initial discontinuity. Moreover, the interactions of non-selfsimilar elementary waves are discussed by respectively taking the initial discontinuity as a parabola and a circle which enable us to provide the global structures of the entropy solutions explicitly.