The generalized nonlinear initial-boundary Riemann problem for quasilinear hyperbolic systems of conservation laws

In this paper, we study the nonlinear initial-boundary Riemann problem and the generalized nonlinear initial-boundary Riemann problem for quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions on the domain {(t,x)|t⩾0,x⩾0}. Under the assumption that each positive eigenvalue is either linearly degenerate or genuinely nonlinear, we get the existence and uniqueness of the self-similar solution to the nonlinear initial-boundary Riemann problem and of the global piecewise C1 solution containing only shocks and (or) contact discontinuities to the corresponding generalized nonlinear initial-boundary Riemann problem. It shows that the self-similar solution to the nonlinear initial-boundary Riemann problem possesses the global structural stability.