Global Structure Stability of Riemann Solution of Quasilinear Hyperbolic System of Conservation Law in Presence of Boundary: Shocks and Contact Discontinuities

Abstract

In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the piecewise C1 solution u = u(t, x) of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U(x/t) of the corresponding Riemann problem. The piecewise C1 solution u = u(t, x) to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.