一阶格点系统的不变测度与Liouville型方程

该文讨论一阶格点系统的解在相空间中的概率分布问题.作者先证明该格点系统的解算子生成的过程存在拉回吸引子,然后证明拉回吸引子上存在唯一的Borel不变概率测度,且该不变测度满足Liouville型方程.     

Liouville Type Theorems for Nonlinear p-Laplacian Equation on Complete Noncompact Riemannian Manifolds*

In this paper,the authors study the gradient estimates for positive weak solutions to the following p-Laplacian equation △_pu+au^σ=0 on complete noncompact Riemannian manifold,where a,σ are two nonzero real constants with p≠2.Using the gradient estimate,they can get the corresponding Lionville theorem.On the other hand,by virtue of the Poincare inequality,they also obtain a Liouville theorem under some integral conditions with respect to positive weak solutions.     

一维Allen-Cahn方程紧差分格式的离散最大化原则和能量稳定性研究

本文主要研究相场模拟中的Allen-Cahn模型,考虑一维Allen-Cahn方程紧差分方法的数值逼近.建立具有O(∫τ2+h4)精度的全离散紧差分格式,证明在合理的步长比和时间步长的约束下,其数值解满足离散最大化原则,在此基础上,研究了全离散格式的能量稳定性.最后给出数值算例.     

On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations

It is proved that the Dirichlet problem is correct in the characteristic rectangle D _ab = [0, a] × [0, b] for the linear hyperbolic equation

具色散耗散项的四阶波动方程解的渐近性质

研究具色散和耗散项的四阶波动方程的初边值问题．使用乘子法,证明了问题的整体强解在关于非线性项简单而宽泛的假设下,随时间趋于无穷而衰减到零．     

On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations

In the rectangle D = (0,

Multi-Symplectic Fourier Pseudospectral Method for a Higher Order Wave Equation of KdV Type

The higher order wave equation of KdV type, which describes many important physical phenomena, has been investigated widely in last several decades. In this work, multi-symplectic formulations for the higher order wave equation of KdV type are presented, and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is calculated by the multi-symplectic Fourier pseudospectral scheme. Numerical experiments are carried out, which verify the efficiency of the Fourier pseudospectral method.     

一类四阶奇异微分方程正解存在的充分必要条件

通过Green函数给出了一对具体的上下解,对一类奇异微分方程边值问题做了研究,得到正解存在的充分必要条件.     

A Discrete Phenomenon in the C and Analytic Regularity of the Blow-Up Curve of Solutions to the Liouville Equation in One Space Dimension

We give a complete discussion of the C^∞ or analytic regularity of blow-up curves for Cauchy problems or some mixed problems for the Liouville equation in one space dimension. In the case of mixed problems, the regularity results depend on the boundary condition: actually, we show the existence of a sequence of boundary conditions for which the regularity of the blow-up curve is better than in the general case.     

含连续时滞和阻尼项的二阶半线性微分方程解的振动性

研究了一类含有连续分布时滞和阻尼项的二阶半线性微分方程运用Riccati变换和H函数方法,获得了该方程解的振动性的若干充分条件.     

Harnack Differential Inequalities for the Parabolic Equation ut=LF(u) on Riemannian Manifolds and Applications

In this paper, let(M~n, g) be an n-dimensional complete Riemannian manifold with the mdimensional Bakry–mery Ricci curvature bounded below. By using the maximum principle, we first prove a Li–Yau type Harnack differential inequality for positive solutions to the parabolic equation u_t= LF(u)=ΔF(u)-f·F(u),on compact Riemannian manifolds Mn, where F∈C~2(0, ∞), F0 and f is a C~2-smooth function defined on M~n. As application, the Harnack differential inequalities for fast diffusion type equation and porous media type equation are derived. On the other hand, we derive a local Hamilton type gradient estimate for positive solutions of the degenerate parabolic equation on complete Riemannian manifolds. As application, related local Hamilton type gradient estimate and Harnack inequality for fast dfiffusion type equation are established. Our results generalize some known results.     

二类1错误矩阵方程增优置换变换求解及其在城市交通管理中的应用研究

消错学的错误矩阵可表达错误逻辑里所定义的分解、相似、增加、置换、毁灭、单位变换等转化词,针对其中的置换变换,构建了二类1错误矩阵方程增优置换变换错误矩阵方程,并讨论了该类错误矩阵方程的求解.用交通管理问题对错误矩阵进行了举例,并构建相应的错误矩阵方程,利用上述的求解方法,对二类1方程置换变换进行了求解.