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1.
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.  相似文献   

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This paper concerns the asymptotic structure of the scintillation function in the simplified setting of wave propagation modeled by an Itô–Schrödinger equation. We show that the size of the scintillation function crucially depends on the smoothness of the initial conditions for the wave equation and on the size of the “array of detectors” where the wave fields are measured. In many practical settings, we show that the estimates are optimal and devise an equation for the appropriately rescaled scintillation function. The estimates are based on a careful analysis of Wigner transforms and of linear kinetic equations involving oscillatory integrals.  相似文献   

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Mathematical Programming models have been suggested as a tool for optimal media selection. In order to accommodate several objective functions goal programming models have been put forward. It seems, however, that these models are not yet operational and efficient enough to be used in practice.Based on these approaches a model is suggested which seems to be suited to map appropriately fuzzy and subjective phenomena and which is flexible enough to incorporate several criteria (objective functions) simultaneously.An interactive use is envisaged which would help to adapt the model easily to different real world conditions.  相似文献   

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We consider a nonlinear viscoelastic wave equation with nonlinear source term. Under suitable conditions on g, it is proved that any weak solution with negative initial energy blows up in finite time if p>2.  相似文献   

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《大学数学》2015,(4):90-94
线性流形作为n维数组向量空间的子集合,与线性方程组的解和n维数组向量空间的子空间有着密切的联系.通过讨论线性流形的一些基本性质,研究其与线性方程组的解,线性子空间的关系,从而加深对这一概念的理解.  相似文献   

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一维粘弹性波动方程弹性系数的识别方法   总被引:2,自引:0,他引:2  
丛文相 《应用数学》1998,11(1):128-130
本文就一维粘弹性波动方程弹性系数的求解问题,给出了一个新的求解方法.通过对算法进行分析可知,该方法具有较小的计算量,并且具较好的数值稳定性.数值模拟表明了该方法的可行性及有效性.  相似文献   

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A singular perturbation method is developed to investigate onedimensional weak nonlinear waves in dissipative or dispersivemedia. Utilizing this method a boundary value problem for asystem of partial differential equations characterizing wavepropagation in homogeneous dissipative or dispersive media isstudied. In order to obtain a first-order uniformly valid solution,the problem is reduced to an initial value problem for scalarnon-linear partial differential equation. Some special casesarising from the structure of coefficient matrices are examinedand the method is extended to these cases. As an applicationof the perturbation method, various problems of wave propagationin a finite linear viscoelastic half-space are studied.  相似文献   

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In this paper, we consider the one-dimensional inhomogeneous wave equation with particular focus on its spectral asymptotic properties and its numerical resolution. In the first part of the paper, we analyze the asymptotic nodal point distribution of high-frequency eigenfunctions, which, in turn, gives further information about the asymptotic behavior of eigenvalues and eigenfunctions. We then turn to the behavior of eigenfunctions in the high- and low-frequency limit. In the latter case, we derive a homogenization limit, whereas in the first we show that a sort of self-homogenization occurs at high frequencies. We also remark on the structure of the solution operator and its relation to desired properties of any numerical approximation. We subsequently shift our focus to the latter and present a Galerkin scheme based on a spectral integral representation of the propagator in combination with Gaussian quadrature in the spectral variable with a frequency-dependent measure. The proposed scheme yields accurate resolution of both high- and low-frequency components of the solution and as a result proves to be more accurate than available schemes at large time steps for both smooth and nonsmooth speeds of propagation.  相似文献   

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The stress singularities that evolve at the corner of a notchedviscoelastic angular plate subject to mode I deformation isdiscussed when prescribed, but arbitrary, displacements aresymmetrically applied to both radial edges of the sector. Thesolution procedure, based on Laplace and Mellin transforms (withtransform parameters p and s, respectively), leads to an eigenvalueproblem in the complex p-plane, which is dependent on Poisson'sratio and characterizes the singular behaviour of the stressfields. Although simple solutions to the transcendental eigenequationare not available, the real-time evolution of the stress concentrationsis obtained by monitoring a particular branch of the eigenvalueequation as it moves in the complex p-plane. A correspondingpath is traced in an appropriately cut strip in the s-plane,in which solutions to the eigenequation are single-valued. Analyticcontinuation in the p-plane thus allows the Laplace and Mellininversions to be performed and the real-time behaviour of theplane-stress components to be expressed as contour integralswithin the strips in the complex s-plane. Cast in this form,the stress components are evaluated numerically when the viscoelasticmaterial is represented as a standard linear solid. Their dependenceon the angular variation within the plate, the applied load,and the effects of the viscoelastic material properties is exhibitedfor a number of situations, and in each case contrasted withshort- and long-time asymptotic curves based on Tauberian theorems.  相似文献   

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考虑回归模型yi=x′iβ+ g(ti) + ei, 0 ≤i ≤nr=Rβ其中(xi,ti)是固定非随机设计点列,xi=(xi1,…,xip)′,β=(β1,…,βp)′(p 1) ,g是定义在[0 ,1]上的未知函数,β是未知待估参数,0≤ ti≤1i,ei 是i.i.d随机误差,且Eei=0 ,Ee2i=σ2 <∞.r是一个J维向量,R是一个J* p列满秩矩阵,基于g的估计取一个非参数权估计,本文讨论了在线性约束下β的最小二乘估计的相合性及渐近正态性.  相似文献   

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Part II is a continuation of Part I published in Zapiski Nauchnykh Seminarov POMI, Vol. 273 (JOurnal of Mathematical Sciences, Vol. 116, No. 2, 2003).  相似文献   

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In this paper a generalisation of the notion of polarity is exhibited which allows to completely describe, in an incidence-geometric way, the linear complexes of h-subspaces. A generalised polarity is defined to be a partial map which maps (h−1)-subspaces to hyperplanes, satisfying suitable linearity and reciprocity properties. Generalised polarities with the null property give rise to linear complexes and vice versa. Given that there exists for h > 1 a linear complex of h-subspaces which contains no star – this seems to be an open problem over an arbitrary ground field – the combinatorial structure of a partition of the line set of the projective space into non-geometric spreads of its hyperplanes can be obtained. This line partition has an additional linearity property which turns out to be characteristic. Received: December 3, 2007. Revised: December 13, 2007.  相似文献   

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流体饱和多孔介质中波传播问题的有限元分析   总被引:3,自引:1,他引:3  
采用基于混合物理论的多孔介质模型,给出流体饱和两相多孔介质波动问题的有限元分析方法· 采用罚方法导出的有限元动力方程,时间积分可采用显式和隐式积分两种方案· 用编制的有限元程序分析了一维柱体在跃阶载荷和脉冲载荷作用下的波传播问题,得到该两种瞬态载荷作用下固体和流体相位移、速度以及固体相有效应力和孔隙压力随时间的变化关系,并对波的传播现象进行了分析· 所得结果与理论相吻合·  相似文献   

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The results of a preliminary study of a particular nonlinear system of partial differential equations are presented. While much of this work pertains to two coupled nonlinear Schrödinger equations, it is believed that the properties found are representative of many other dispersive wave systems.  相似文献   

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