In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A suffic...In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.展开更多
In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on th...In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.展开更多
This paper deals with the asymptotic behavior of global classical solutions to quasilinear hyperbolic systems of diagonal form with weakly linearly degenerate characteristic fields. On the basis of global existence an...This paper deals with the asymptotic behavior of global classical solutions to quasilinear hyperbolic systems of diagonal form with weakly linearly degenerate characteristic fields. On the basis of global existence and uniqueness of C^1 solution, we prove that the solution to the Cauchy problem approaches a combination of C^1 traveling wave solutions when t tends to the infinity.展开更多
文摘In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.
基金Supported by the National Natural Science Foundation of China (Grant No.10771038)
文摘In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.
基金Supported by the Doctoral Programme Foundation of the Ministry of Education of China (Grant No.20070246-173)
文摘This paper deals with the asymptotic behavior of global classical solutions to quasilinear hyperbolic systems of diagonal form with weakly linearly degenerate characteristic fields. On the basis of global existence and uniqueness of C^1 solution, we prove that the solution to the Cauchy problem approaches a combination of C^1 traveling wave solutions when t tends to the infinity.
