In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the probl...In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method.展开更多
This paper gives the suffcient conditions of blow-up of the solution of a nonlinear hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local so...This paper gives the suffcient conditions of blow-up of the solution of a nonlinear hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local solution of the problem.展开更多
A new polynomial formulation of variable step size linear multistep methods is pre- sented, where each k-step method is characterized by a fixed set of k - 1 or k parameters. This construction includes all methods of ...A new polynomial formulation of variable step size linear multistep methods is pre- sented, where each k-step method is characterized by a fixed set of k - 1 or k parameters. This construction includes all methods of maximal order （p = k for stiff, and p = k ＋ 1 for nonstiff problems）. Supporting time step adaptivity by construction, the new formulation is not based on extending classical fixed step size methods; instead classical methods are obtained as fixed step size restrictions within a unified framework. The methods are imple- mented in MATLAB, with local error estimation and a wide range of step size controllers. This provides a platform for investigating and comparing different multistep method in realistic operational conditions. Computational experiments show that the new multi- step method construction and implementation compares favorably to existing software, although variable order has not yet been included.展开更多
In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a ...In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away from the shock discontinuity and the boundary at a rate of ε1 as the viscosity ε tends to zero.展开更多
基金A Project Supported by Scientific Research Fund of Hunan Provincial Education Department (10C1056)Scientific Research Found of Huaihua University (HHUY2011-01)
文摘In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method.
基金Supported by the National Natural Science Foundation of China（10671182） Supported by the Excellent Youth Teachers Foundation of High College of Henan Province（2006110016）
文摘This paper gives the suffcient conditions of blow-up of the solution of a nonlinear hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local solution of the problem.
文摘A new polynomial formulation of variable step size linear multistep methods is pre- sented, where each k-step method is characterized by a fixed set of k - 1 or k parameters. This construction includes all methods of maximal order （p = k for stiff, and p = k ＋ 1 for nonstiff problems）. Supporting time step adaptivity by construction, the new formulation is not based on extending classical fixed step size methods; instead classical methods are obtained as fixed step size restrictions within a unified framework. The methods are imple- mented in MATLAB, with local error estimation and a wide range of step size controllers. This provides a platform for investigating and comparing different multistep method in realistic operational conditions. Computational experiments show that the new multi- step method construction and implementation compares favorably to existing software, although variable order has not yet been included.
基金Acknowledgments The author is supported by Tianyuan Foundation （No. 11026093） and the National Natural Science Foundation of China （Nos. 11101162, 11071086）.
文摘In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away from the shock discontinuity and the boundary at a rate of ε1 as the viscosity ε tends to zero.
