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 the authors prove the existence and uniqueness of global classical solutions to some kinds of typical boundary-value problems and typical free-boundary problems for quasilinear hyperbolic systems.
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
In this paper, we prove the existence of the global smooth solution to the Cauchy problems for a class of diagonalizable high dimensional quasilinear hyperbolic systems consisted of n-equations.
Ⅰ. INTRODUCTIONWhen a supersonic flow passes a thin wing with a small attack angle, there will appear an attached shock front issued from the head edge of the wing. To determine the place of the shock front and the f...Ⅰ. INTRODUCTIONWhen a supersonic flow passes a thin wing with a small attack angle, there will appear an attached shock front issued from the head edge of the wing. To determine the place of the shock front and the flow field behind the shock up to the surface of the展开更多
The author studies M-D Riemann problems for a quasilinear nonstrictly hyperbolic system. The initial data are taken as three different constants in three sections divided by three rays starting from the origin. From ...The author studies M-D Riemann problems for a quasilinear nonstrictly hyperbolic system. The initial data are taken as three different constants in three sections divided by three rays starting from the origin. From each direction of these rays two waves coming from infinity are allowed. All possible local singularity structures are carefully studied and classified. Then based on such analysis,existence and global singularity structure of the solution are obtained under some assumptions.展开更多
In this paper, the synchronization for a kind of first order quasilinear hyperbolic system is taken into account. In this system, all the equations share the same positive wave speed. To realize the synchronization, a...In this paper, the synchronization for a kind of first order quasilinear hyperbolic system is taken into account. In this system, all the equations share the same positive wave speed. To realize the synchronization, a uniform constructive method is adopted, rather than an iteration process usually used in dealing with nonlinear systems. Furthermore,similar results on the exact boundary synchronization by groups can be obtained for a kind of first order quasilinear hyperbolic system of equations with different positive wave speeds by groups.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.
文摘In this paper the authors prove the existence and uniqueness of global classical solutions to some kinds of typical boundary-value problems and typical free-boundary problems for quasilinear hyperbolic systems.
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.
文摘In this paper, we prove the existence of the global smooth solution to the Cauchy problems for a class of diagonalizable high dimensional quasilinear hyperbolic systems consisted of n-equations.
文摘Ⅰ. INTRODUCTIONWhen a supersonic flow passes a thin wing with a small attack angle, there will appear an attached shock front issued from the head edge of the wing. To determine the place of the shock front and the flow field behind the shock up to the surface of the
文摘The author studies M-D Riemann problems for a quasilinear nonstrictly hyperbolic system. The initial data are taken as three different constants in three sections divided by three rays starting from the origin. From each direction of these rays two waves coming from infinity are allowed. All possible local singularity structures are carefully studied and classified. Then based on such analysis,existence and global singularity structure of the solution are obtained under some assumptions.
文摘In this paper, the synchronization for a kind of first order quasilinear hyperbolic system is taken into account. In this system, all the equations share the same positive wave speed. To realize the synchronization, a uniform constructive method is adopted, rather than an iteration process usually used in dealing with nonlinear systems. Furthermore,similar results on the exact boundary synchronization by groups can be obtained for a kind of first order quasilinear hyperbolic system of equations with different positive wave speeds by groups.
