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981.
莫嘉琪 《应用数学和力学(英文版)》2009,30(11):1455-1460
A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existence and the asymptotic behavior of the solution to the boundary value problem are studied, In the present paper, the solution to the original singularly perturbed problem with two parameters has only one boundary layer. 相似文献
982.
莫嘉琪 《应用数学和力学(英文版)》2009,30(8):1003-1008
In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed in relation to two small parameters. The asymptotic solutions of the problem are given. 相似文献
983.
常规位移有限元的结构振动方程是n个二阶常微分方程组.采用一般交分原理推导,将结构振动问题引入Hamiltoil体系,将得到2n个一阶常微分方程组.精细积分法宜于处理一阶方程,应用于线性定常结构动力问题求解,可以得到在数值上逼近精确解的结果.对于非齐次动力方程,当结构具有刚体位移时,系统矩阵将出现奇异.本文借鉴全元选大元高斯-约当法求解线性方程组的经验,提出全元选大元法求奇异矩阵零本征解的方法,该方法可以简便快速地寻求奇异矩阵零本征值对应的子空间.利用Hamiltoil体系已有研究成果及Hamilton系统的共轭辛正交归一关系,迅速将零本征值对应的子空间分离出来,通过投影排除奇异部分,然后用精细积分法求得问题的解.数值算例表明,该方法对Hamilton系统奇异问题,处理方便,计算量小,易于实现,同时保持了精细算法的优点. 相似文献
984.
A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalities, the existence and the asymptotic behavior of the solution to the initial boundary value problem are studied. 相似文献
985.
This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters. 相似文献
986.
In this paper, we present the solution of the Klein--Gordon equation. Klein--Gordon equation is the relativistic version of the Schrödinger equation, which is used to describe spinless particles. The He’s variational iteration method (VIM) is implemented to give approximate and analytical solutions for this equation. The variational iteration method is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. Application of variational iteration technique to this problem shows rapid convergence of the sequence constructed by this method to the exact solution. Moreover, this technique reduces the volume of calculations by avoiding discretization of the variables, linearization or small perturbations. 相似文献
987.
AUV组合导航系统信息匹配的可观测度 总被引:2,自引:2,他引:0
针对自主水下潜器(AUV)导航的特点和需求,设计了一种捷联惯导/多普勒/磁罗经/地形匹配组合导航系统(SINS/DVL/MCP/TAN),同时对AUV组合导航的两种信息匹配方式进行了基于动态系统奇异值分解的可观测度研究以评估该组合导航的Kalman滤波的估计能力。可观测度研究结果说明该组合导航能显著提高AUV的航向角误差和位置误差的可观测度,从而可以提高AUV的航向和位置精度。Kalman滤波的仿真结果验证了该结论的正确性,表明了该细合导航系统的Kalman滤波的估计能力强,能够得到较高精度的位置、速度和姿态信息,可以满足AUV长时间远距离导航的需要。 相似文献
988.
989.
In this article we make a full study of the class of non-degenerate real planar quadratic differential systems having all
points at infinity (in the Poincaré compactification) as singularities. We prove that all such systems have invariant affine
lines of total multiplicity 3, give all their configurations of invariant lines and show that all these systems are integrable
via the method of Darboux having cubic polynomials as inverse integrating factors. After constructing the topologically distinct
phase portraits in this class we give invariant necessary and sufficient conditions in terms of the 12 coefficients of the
systems for the realization of each one of them and give representatives of the orbits under the action of the affine group
and time rescaling. We construct the moduli space of this class for this action and give the corresponding bifurcation diagram.
Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday 相似文献
990.
S.M. Nagiyev E.I. Jafarov M.Y. Efendiyev 《理论物理通讯》2008,49(2):315-318
The SU(1,1) coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU(1,1) coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr Sommerfeld quantization rule yields the exact expression for the energy spectrum. 相似文献