The riemann problem for a two-dimensional hyperbolic system of conservation laws with non-classical weak solutions: some one-J and non-R initital data

摘要

The Riemann problem for a two-dimensional 2x2 nonstrictly hyperbolic sys- tem of nonlinear conservation laws has been considered for constant initial data having discontinuities on three rays with vertex at the origin. The solutions are constructed for some one-J and non-R initial data. One kind of new discontinuity, which is labelled as the δ-shock wave, appears in some solutions. The δ-shock wave is a discontinuity plane that is the support of a generalized function.