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 pieeew...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 pieeewise C^1 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 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 contact discontinuities, but no rarefaction waves and other weak discontinuities.展开更多
In this paper,we consider a kind of quasilinear hyperbolic systems with inhomogeneous terms satisfying dissipative condition or matching condition.For the Cauchy problem of this kind of systems,we prove that,if the in...In this paper,we consider a kind of quasilinear hyperbolic systems with inhomogeneous terms satisfying dissipative condition or matching condition.For the Cauchy problem of this kind of systems,we prove that,if the initial data is small and satisfies some decay condition,and the system is weakly linearly degenerate,then the Cauchy problem admits a unique global classical solution on t ≥ 0.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10671124
文摘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 pieeewise C^1 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 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 contact discontinuities, but no rarefaction waves and other weak discontinuities.
基金Supported by National Science Foundation of China（10671124）
文摘In this paper,we consider a kind of quasilinear hyperbolic systems with inhomogeneous terms satisfying dissipative condition or matching condition.For the Cauchy problem of this kind of systems,we prove that,if the initial data is small and satisfies some decay condition,and the system is weakly linearly degenerate,then the Cauchy problem admits a unique global classical solution on t ≥ 0.
