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

摘要

In this paper,we investigate a class of mixed initial-boundary value problems for a kind of n×n quasilinearhyperbolic systems of conservation laws on the quarter plan.We show that the structure of the piecewise C^1 solutionu = u(t,x) of the problem,which can be regarded as a perturbation of the corresponding Riemann problem,is globallysimilar to that of the solution u=U(x/t) of the corresponding Riemann problem.The piecewise C^1 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 contactdiscontinuities,but no rarefaction waves and other weak discontinuities.