一类具广义边界条件参数方程的解

~~     

非线性中子输运方程的Galerkin有限元解

§1.引言在核反应系统中,当中子数目足够多时,中子间的相互作用必须考虑,这就导致非线性中子输运方程。在这方面,已出现了一些研究工作,文献[1]对一类非线性中子输运方程,在一定的假定下,用半群方法证明了它的初边值问题解的存在性和唯一性。本文试图用[2]中的方法考察非线性中子输运方程的Galerkin有限元解。在§2中,给出了解的先验估计。在§3中,利用解的先验估计给出了广义解的存在性,构造了Galer-     

迁移方程的扩散近似的收敛性

导出了迁移方程的扩散近似方程．说明了它的离散纵标方法在区间内和边界上都有扩散极限，它的解关于一致地收敛于迁移方程的解．其收敛性的证明是依据其渐近扩散展开式，在边界层上得到的误差估计逼近其离散纵标方法的解．     

一类广义Sine—Gordon方程的解的存在唯一性

本文利用非线性Ｇａｌｅｒｋｉｎ方法,证明了一类广义Ｓｉｎｅ－Ｇｏｒｄｏｎ方程在Ｄｉｒｉｃｈｌｅｔ边值条件下的整体解的存在唯一性．     

测度空间上非线性中子迁移方程的适定性和渐近性

本文给出测定空间上非线性中子迁移方程的适定性的充分条件及渐近性质．     

非定常Navier-Stokes方程的稳定化特征有限元法

1引言特征线有限元法是求解对流扩散问题的有效方法。在处理对流占优问题时,表现出了很好的稳定性[8]。对于求解Navier-Stokes方程,文[9]建立了特征有限元格式,并进行了详细分析,但得到的收敛阶O(h~m △t (h~(m 1)/△t))只是拟丰满的。文[10]对此作了非线性稳定性的进一步分析,给出了关于速度和压力的最优误差估计。但目前所有的特征有限元法都要求有限元空间满足inf-sup条件,这就排除了工程实际应用计算方便的低阶有     

一维广义Ginzburg-Landau方程解的正则性及线性与非线性Galerkin近似

本文得到了一维广义Ginzburs－Landau方程解的Gevrey类正则性和关于时间的解析性．在此基础上得到线性Galerkin近似和非线性Galerkin近似的收敛性．     

具有非局部边值约束的中子迁移问题单调衰减解

中子迁移方程是核动力学中描述中子的分布过程.本文讨论具有非局部边值约束的含任意空穴的非均匀介质中具连续能量的中子迁移系统其中D_1是R~3中含任意空穴的有界凸区域,且其边界(?)D_1分片光滑,D_2是R~3中有界可测集,表示位于x=(x_1,X_2,X-3)处,具有速度v=(v_1,v_2,v_3)在时刻t的中子分布密度.N_0(x,v)是初始分布,σ(x,v)表示含任意空穴的非均匀介质的总截面,k(x,v,v′)是能量迁移核,f(x,y)是边界约束函数,σ、k、N_0、f均为非负连续有界函数.另记     

线性算子方程广义解的存在性

本文中我们研究并得到了线性算子方程的Moore-Penrose广义解的稳定性性质。     

中子测井问题中非定常输运方程的谱流线扩散有限元耦合方法

针对中子测井问题,研究非定常Boltamann中子输运方程的确定型数值求解方法,给出了求解Boltzmann方程的球谐函数展开和流线扩散有限元耦合方法,证明了这种耦合方法的收敛性和误差估计。实际算例表明此方法是有效的。     

Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media

Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space $(\mathcal{P}_k(K), \mathcal{P}_{k−1}(∂K), [\mathcal{P}_{k−1}(K)]^2).$ Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in $L^∞(L^2)$ norm. This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes. Finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.     

Alternating Direction Implicit Galerkin Finite Element Method for the Two-Dimensional Time Fractional Evolution Equation

New numerical techniques are presented for the solution of the two-dimensional time fractional evolution equation in the unit square. In these methods, Galerkin finite element is used for the spatial discretization, and, for the time stepping, new alternating direction implicit (ADI) method based on the backward Euler method combined with the first order convolution quadrature approximating the integral term are considered. The ADI Galerkin finite element method is proved to be convergent in time and in the $L^2$ norm in space. The convergence order is$\mathcal{O}$($k$|ln $k$|+$h^r$), where $k$ is the temporal grid size and $h$ is spatial grid size in the $x$ and $y$ directions, respectively. Numerical results are presented to support our theoretical analysis.     

A New Compact Finite Difference Method for Solving the Generalized Long Wave Equation

The aim of this article is to analyze a new compact finite difference method (CFDM) for solving the generalized regularized long wave (GRLW) equation. This method leads to a system of linear equations involving tridiagonal matrices and the rate of convergence of the method is of order O(k ² + h ⁴) where k and h are mesh sizes of time and space variables, respectively. Stability analysis of the method is investigated by the energy method and an error estimate is given. The propagation of single solitons and interaction of two solitary waves are applied to validate the method which is found to be accurate and efficient. Three invariants of the motion are evaluated to determine conservation properties of the method.     

Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation

The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.     

Error Estimates for Semi-Discrete and Fully Discrete Galerkin Finite Element Approximations of the General Linear Second-Order Hyperbolic Equation

In this article, we derive error estimates for the semi-discrete and fully discrete Galerkin approximations of a general linear second-order hyperbolic partial differential equation with general damping (which includes boundary damping). The results can be applied to a variety of cases (e.g. vibrating systems of linked elastic bodies). The results generalize pioneering work of Dupont and complement a recent article by Basson and Van Rensburg.     

一个广义薄膜方程弱解的存在性

讨论一个广义薄膜方程,在一些初值的假定下,用时间离散化方法证明其弱解的存在性.     

广义Pochhammer-Chree方程的新孤波解和余弦周期波解

本文利用假设待定法求出了具5阶非线性项的广义Pochhammer-Chree方程具双曲正割函数分式形式的2个新孤波解和6个余弦函数周期波解,并分别给出了它们的有界性条件.揭示了行波波速v的改变与钟状孤波解和余弦周期波解波形变化的相关性.     

广义Hasegawa-Mima方程整体解的存在惟一性

运用关于时间的一致先验估计,证明了具有周期边值条件的广义Hasegawa-Mima方程整体解的存在性、惟一性.