一阶半线性双曲型方程组的精确边界能控性与能观性

本文以一阶半线性双曲型方程组混合初边值问题的整体C~1解理论为基础,采用直接构造的方法建立了一阶半线性双曲组的整体精确边界能控性及能观性理论,对于相应的控制及观测时间给出了精确的估计,并揭示了精确能控性与能观性之间隐含的某种对偶关系。本文还揭示了在非自治系统的情形下,精确能控性与能观性的对偶关系有可能会丧失。     

二阶拟线性双曲型方程组的精确边界能控性

本文利用具零特征的一阶拟线性双曲型方程组带一般非线性边界条件的混合初-边值问题的半整体C^1解的存在唯一性,对具一般类型非线性边界条件的二阶拟线性双曲型方程组建立了精确边界能控性。     

二阶拟线性双曲型方程的精确能观性

在一阶拟线性双曲组混合初边值问题半整体C1解理论的基础上,本文针对一般二阶拟线性双曲型方程的特征根在平衡态附近的不同分布情况,在具有一般边界条件的情况下,分别得到了相应的精确能观性及能观不等式.     

二阶拟线性双曲型方程的精确边界能控性

本文以二阶拟线性双曲型方程混合初边值问题的半整体C~2解理论为基础,针对一般的二阶拟线性双曲型方程的特征根在平衡态附近的不同分布情况,分别提出了相应的一般边界条件,并采用直接构造的方法,对特征根均不为零的情况,建立了完整的局部精确边界能控性理论;对一特征根为零的情况,对一类特殊的方程建立了其精确边界能控的充分必要条件,并分别对相应的控制时间给出了估计.     

一阶拟线性双曲型方程组Goursat问题经典解的破裂机制(英文)

对一阶拟线性双曲型方程组的Goursat问题,利用特征线方法及波分解公式,在方程组不是弱线性退化的假设下,当特征边界上给出的边界函数C1范数充分小、且满足一定衰减性时,得到其C1解的破裂机制及关于生命跨度的渐近估计.     

拟线性双曲型方程组的间断初始值问题

对于二自变量的拟线性双曲型平衡律方程组的间断初始值问题,本文讨论了其间断解的局部构造,证明了在分块光滑函数类中的局部间断解的存在性与唯一性,该解可包含激波、中心波、接触间断及弱间断。     

具一种非光滑初始数据的非齐次拟线性双曲组的整体弱间断解

本文考虑一阶非齐次拟线性双曲组具有一种非光滑初始数据的Cauchy问题。在非齐次项满足匹配条件的假设下,得到了此问题存在唯一的整体弱间断解的充要条件。     

一类拟线性椭圆方程组正弱解的存在性和不存在性

本文研究了一类拟线性椭圆方程组在有界区域上的边值问题的正弱解的存在性和不存在性。利用方程组的特征值和特征函数分别构造了弱上解和弱下解,通过比较原理证明了弱下解小于弱上解,用上下解方法得到了正弱解的存在性。最后,用反证法证明了正弱解的不存在性,并给出了正弱解的不存在性条件。     

具常重特征拟线性非严格双曲组的经典解的奇性形成

我们考虑具常重特征的非严格拟线性双曲组的Cauchy问题,在初值具有较弱衰减假设下,得到Cauchy问题解的奇性形成。     

具大参数的拟线性双曲组的Canchy问题及其应用

本文研究拟线性双曲型方程组的某些系数变成无穷时的Cauchy问题。证明了解的存在和唯一性定理,并将它应用于可压缩等熵流的方程组。得到了这样的结果:当Mach数的倒→∞时,可压缩流方程组的极限解满足不可压缩流的Euler方程。     

薄壁杆件翘曲剪应力的边界元精确积分解法

用非连续边界元对薄壁杆件的约束扭转进行了分析,推导出了求解边界点二次翘曲函数值的边界积分方程,给出了边界积分方程数值求解时积分计算的精确表达式。数值算例表明:利用边界积分方程方法分析薄壁杆件的约束扭转问题时效率和精度高,同时采用精确积分可以有效的处理"边界层效应"问题。     

Microscale heat conduction in homogeneous anisotropic media: a dual-reciprocity boundary element method and polynomial time interpolation approach

In this paper, a dual-reciprocity boundary element method based on some polynomial interpolations to the time-dependent variables is presented for the numerical solution of a two-dimensional heat conduction problem governed by a third order partial differential equation (PDE) over a homogeneous anisotropic medium. The PDE is derived using a non-Fourier heat flux model which may account for thermal waves and/or microscopic effects. In the analysis, discontinuous linear elements are used to model the boundary and the variables along the boundary. The systems of algebraic equations are set up to solve all the unknowns. For the purpose of evaluating the proposed method, some numerical examples with known exact solutions are solved. The numerical results obtained agree well with the exact solutions.     

一种基于再生核空间解决边值问题的新方法(英文)

在本论文中,我们介绍一种解决奇异摄动两点边值问题新的方法。它的精确解在再生核空间中是以级数形式出现的。同时,存在n项解u_n(x)近似于精确解u(x),并且可以证明u_n(x)收敛于u(x)。我们在此举出一些数列来验证本方法的精确性,用此方法得出的解,显示了这种方法的简单有效。     

Two-dimensional non-Fourier heat conduction with arbitrary initial and periodic boundary conditions

In this paper, the (2+1)-dimensional hyperbolic heat conduction equation is analytically solved under the influence of arbitrary initial conditions for a rectangular plate with homogeneous boundary conditions of first-kind. The temperature field is obtained as a double Fourier series. The presented solution is valid even for discontinuous but integrable initial conditions. Afterwards, the solution is generalized by means of a transformation to cover problems with inhomogeneous first-kind boundary conditions. Another interesting issue is that the obtained solution can be considered as a solution to the Klein–Gordon equation under the influence of arbitrary initial conditions by means of a simple transformation.     

Exact integration in the boundary element method for two-dimensional elastostatic problems

This paper derives the exact integrations for the integrals in the boundary element analysis of two-dimensional elastostatics. For facilitation, the derivation is based on the simple forms of the fundamental functions by taking constant, discontinuous linear and discontinuous quadratic elements as examples. The efficiency and accuracy of the derived exact integrations are verified against five benchmark problems; the results indicate that the derived exact integrations significantly reduces the CPU time for forming the matrices of the boundary element analysis and solving the internal displacements.