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

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.

Global Classical Solutions of Inhomogeneous Quasilinear Hyperbolic Systems

在这份报纸，我们与不同类的条款认为一种 quasilinear 是夸张系统令人满意的消散的状况或匹配的状况。为这种系统的 Cauchy 问题，我们证明如果起始的数据是小的并且满足一些腐烂，状况，和系统是线性地微弱地堕落，那么， Cauchy 问题在 t 上承认一个唯一的全球古典解决方案 0。